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JEE Hyperbola PYQs with Solutions

276 previous year questions from Hyperbola (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

276 questionsMathematics2005–2026Answers + solutions

About Hyperbola PYQs

Hyperbola has 276 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (107), NTA Abhyas JEE Main (40), 99 Percentile Qs Bank for JEE Main (29) and 3 other sources, spanning 2005 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 10
  • 2025: 12
  • 2024: 13
  • 2023: 10
  • 2022: 18
  • 2021: 10
  • 2020: 49
  • 2019: 12
  • 2018: 5
  • 2017: 2
  • 2016: 3
  • 2015: 1

Hyperbola questions with solutions

1

If the eccentricity e of the hyperbola (x^2)/(a^2) - (y^2)/(b^2) = 1 , passing through (6, 4 3 ) , satisfies 15(e^2 + 1) = 34e , then the length of the latus rectum of the

JEE Main 2026 Solution View → 2

Let the eccentricity e of a hyperbola satisfy the equation 6e^2 - 11e + 3 = 0 . If the foci of the hyperbola are (3, 5) and (3, -4) , then the length of its latus rectum is :

JEE Main 2026 Solution View → 3

Let H: (x^2)/(a^2)-(y^2)/(b^2)=1 be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is (8)/(3) . If the line x=α intersects the

JEE Main 2026 Solution View → 4

Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such that the mid point of the line segment PQ is ((1)/(2), -(1)/(2)) . Then the area of the

JEE Main 2026 Solution View → 5

For some θ ∈(0, (π)/(2)) , let the eccentricity and the length of the latus rectum of the hyperbola x^ 2 -y^ 2 ^ 2 θ=8 be e_ 1 and l_ 1 , respectively, and let the eccentricity

JEE Main 2026 Solution View → 6

Let PQ be a chord of the hyperbola x^ 2 4 - y^ 2 b^ 2 =1 , perpendicular to the x -axis such that OPQ is an equilateral triangle, O being the centre of the hyperbola. If the

JEE Main 2026 Solution View → 7

Let the domain of the function f(x)= _ 3 _ 5 _ 7 (9 x-x^ 2 -13) be the interval (m, n) . Let the hyperbola x^ 2 a^ 2 - y^ 2 ~b^ 2 =1 have eccentricity n 3 and the length of the

JEE Main 2026 Solution View → 8

Let P(10,2 15 ) be a point on the hyperbola x^ 2 a^ 2 - y^ 2 ~b^ 2 =1 , whose foci are S and S^ . If the length of its latus rectum is 8, then the square of the area of Δ PSS^ is

JEE Main 2026 Solution View → 9

If the line α x+2 y=1 , where α ∈ ℝ , does not meet the hyperbola x^ 2 -9 y^ 2 =9 , then a possible value of α is:

JEE Main 2026 Solution View → 10

Let the foci of a hyperbola coincide with the foci of the ellipse x^ 2 36 + y^ 2 16 =1 . If the eccentricity of the hyperbola is 5, then the length of its latus rectum is :

JEE Main 2026 Solution View → 11

Let e_1 and e_2 be the eccentricities of the ellipse x^2 ~b^2 + y^2 25 =1 and the hyperbola x^2 16 - y^2 ~b^2 =1 , respectively. If b 5 and e_1 e_2=1 , then the eccentricity of

JEE Main 2025 Solution View → 12

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b, respectively, and one focus and the corresponding directrix of this hyperbola be

JEE Main 2025 Solution View → 13

Consider the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 having one of its focus at P(-3,0) . If the latus ractum through its other focus subtends a right angle at P and a^2 b^2=α 2 -β

JEE Main 2025 Solution View → 14

Let the sum of the focal distances of the point P(4,3) on the hyperbola H: x^2 a^2 - y^2 ~b^2 =1 be 8 (5)/(3) . If for H , the length of the latus rectum is l and the product of

JEE Main 2025 Solution View → 15

If the equation of the hyperbola with foci (4,2) and (8,2) is 3 x^2-y^2-α x+β y+γ=0 , then α+β+γ is equal to _____.

JEE Main 2025 Solution View → 16

Let the product of the focal distances of the point P(4,2 3 ) on the hyperbola H: x^2 a^2 - y^2 ~b^2 =1 be 32 . Let the length of the conjugate axis of H be p and the length of

JEE Main 2025 Solution View → 17

Let one focus of the hyperbola H: x^2 a^2 - y^2 ~b^2 =1 be at ( 10 , 0) and the corresponding directrix be x= 9 10 . If e and l respectively are the eccentricity and the length of

JEE Main 2025 Solution View → 18

If A and B are the points of intersection of the circle x^2+y^2-8 x=0 and the hyperbola (x^2)/(9)-(y^2)/(4)=1 and a point P moves on the line 2 x-3 y+4=0 , then the centroid of

JEE Main 2025 Solution View → 19

Let H_1: x^2 a^2 - y^2 ~b^2 =1 and H_2:- x^2 ~A^2 + y^2 ~B^2 =1 be two hyperbolas having length of latus rectums 15 2 and 12 5 respectively. Let their ecentricities be e_1=

JEE Main 2025 Solution View → 20

Let the circle C touch the line x-y+1=0 , have the centre on the positive x -axis, and cut off a chord of length 4 13 along the line -3 x+2 y=1 . Let H be the hyperbola

JEE Main 2025 Solution View → 21

Let E: x^2 a^2 + y^2 ~b^2 =1, a and H: x^2 ~A^2 - y^2 ~B^2 =1 . Let the distance between the foci of E and the foci of H be 2 3 . If a-A=2 , and the ratio of the eccentricities of

JEE Main 2025 Solution View → 22

Let the foci of a hyperbola be (1,14) and (1,-12) . If it passes through the point (1,6) , then the length of its latus-rectum is :

JEE Main 2025 Solution View → 23

Let the foci of a hyperbola H coincide with the foci of the ellipse E: ((x-1)^2)/(100)+((y-1)^2)/(75)=1 and the eccentricity of the hyperbola H be the reciprocal of the

JEE Main 2024 Solution View → 24

Let S be the focus of the hyperbola (x^2)/(3)-(y^2)/(5)=1 , on the positive x -axis. Let C be the circle with its centre at A( 6 , 5 ) and passing through the point S . If O is

JEE Main 2024 Solution View → 25

Let H: (-x^2)/(a^2)+(y^2)/(b^2)=1 be the hyperbola, whose eccentricity is 3 and the length of the latus rectum is 4 3 . Suppose the point (α, 6), α>0 lies on H . If β is the

JEE Main 2024 Solution View → 26

The length of the latus rectum and directrices of a hyperbola with eccentricity e are 9 and x= ± 4 13 , respectively. Let the line y- 3 x+ 3 =0 touch this hyperbola at (x_0, y_0)

JEE Main 2024 Solution View → 27

Consider a hyperbola H having centre at the origin and foci on the x -axis. Let C_1 be the circle touching the hyperbola H and having the centre at the origin. Let C_2 be the

JEE Main 2024 Solution View → 28

Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements is -3 . If the points (x, y) satisfying A^2+x ~A+y I=O lie on a hyperbola, whose length of

JEE Main 2024 Solution View → 29

Let x ^ 2 a ^ 2 + y ^ 2 b ^ 2 = 1, a > b be an ellipse, whose eccentricity is 1 2 and the length of the latus rectum is 14 . Then the square of the eccentricity of x ^ 2 a ^ 2 - y

JEE Main 2024 Solution View → 30

For 0 < θ < π / 2 , if the eccentricity of the hyperbola x ^ 2 - y ^ 2 cosec ^ 2 θ = 5 is 7 times eccentricity of the ellipse x ^ 2 cosec ^ 2 θ + y ^ 2 = 5 , then the value of θ

JEE Main 2024 Solution View → 31

If the foci of a hyperbola are same as that of the ellipse x ^ 2 9 + y ^ 2 25 = 1 and the eccentricity of the hyperbola is (15)/(8) times the eccentricity of the ellipse, then the

JEE Main 2024 Solution View → 32

Let the foci and length of the latus rectum of an ellipse x ^ 2 a ^ 2 + y ^ 2 b ^ 2 = 1 , a > b be (± 5, 0) and 50 , respectively. Then, the square of the eccentricity of the

JEE Main 2024 Solution View → 33

Let P be a point on the hyperbola H: x ^ 2 9 - y ^ 2 4 = 1 , in the first quadrant such that the area of triangle formed by P and the two foci of H is 2 13 . Then, the square of

JEE Main 2024 Solution View → 34

Let the latus rectum of the hyperbola x ^ 2 9 - y ^ 2 b ^ 2 = 1 subtend an angle of (π)/(3) at the centre of the hyperbola. If b ^ 2 is equal to (l)/(m) ( 1 + n ) , where l and m

JEE Main 2024 Solution View → 35

Let e _ 1 be the eccentricity of the hyperbola x ^ 2 16 - y ^ 2 9 = 1 and e _ 2 be the eccentricity of the ellipse x ^ 2 a ^ 2 + y ^ 2 b ^ 2 = 1, a > b , which passes through the

JEE Main 2024 Solution View → 36

The foci of a hyperbola are ( ± 2, 0 ) and its eccentricity is (3)/(2) . A tangent, perpendicular to the line 2x + 3y = 6 , is drawn at a point in the first quadrant on the

JEE Main 2023 Solution View → 37

Let m _ 1 and m _ 2 be the slopes of the tangents drawn from the point P(4, 1) to the hyperbola H: y ^ 2 25 - x ^ 2 16 = 1 If Q is the point from which the tangents drawn to H

JEE Main 2023 Solution View → 38

Let the tangent to the parabola y ^ 2 = 12x at the point (3, α) be perpendicular to the line 2x + 2y = 3 . Then the square of distance of the point (6, - 4) from the normal to the

JEE Main 2023 Solution View → 39

Let H _ n : x ^ 2 1 + n - y ^ 2 3 + n = 1, n ∈ ℕ . Let k be the smallest even value of n such that the eccentricity of H _ k is a rational number. If l is the length of the latus

JEE Main 2023 Solution View → 40

Let R be a rectangle given by the lines x = 0, x = 2 , y = 0 and y = 5 . Let A(α, 0) and B(0, β), α ∈ [0, 2] and β ∈ [0, 5] , be such that the line segment AB divides the area of

JEE Main 2023 Solution View → 41

Let the eccentricity of an ellipse x ^ 2 a ^ 2 + y ^ 2 b ^ 2 = 1 is reciprocal to that of the hyperbola 2 x ^ 2 - 2 y ^ 2 = 1 . If the ellipse intersects the hyperbola at right

JEE Main 2023 Solution View → 42

Let P( x _ 0 , y _ 0 ) be the point on the hyperbola 3 x ^ 2 - 4 y ^ 2 = 36 , which is nearest to the line 3x + 2y = 1 . Then 2 ( y _ 0 - x _ 0 ) is equal to :

JEE Main 2023 Solution View → 43

Let H be the hyperbola, whose foci are (1 ± 2 , 0) and eccentricity is 2 . Then the length of its latus rectum is:

JEE Main 2023 Solution View → 44

If the maximum distance of normal to the ellipse x ^ 2 4 + y ^ 2 b ^ 2 = 1, b < 2 , from the origin is 1 , then the eccentricity of the ellipse is:

JEE Main 2023 Solution View → 45

The vertices of a hyperbola H are (± 6, 0) and its eccentricity is 5 2 . Let N be the normal to H at a point in the first quadrant and parallel to the line 2 x + y = 2 2 . If d is

JEE Main 2023 Solution View → 46

Consider the hyperbola x ^ 2 100 - y ^ 2 64 = 1 with foci at S and S _ 1 , where S lies on the positive x -axis. Let P be a point on the hyperbola, in the first quadrant. Let ∠ SP

JEE Advanced 2022 Solution View → 47

Let the focal chord of the parabola P: y ^ 2 = 4x along the line L: y = mx + c, m > 0 meet the parabola at the points M and N . Let the line L be a tangent to the hyperbola H: x ^

JEE Main 2022 Solution View → 48

Let the hyperbola H: x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 pass through the point (2 2 , - 2 2 ) . A parabola is drawn whose focus is same as the focus of H with positive abscissa and the

JEE Main 2022 Solution View → 49

For the hyperbola H: x ^ 2 - y ^ 2 = 1 and the ellipse E: x ^ 2 a ^ 2 + y ^ 2 b ^ 2 = 1, a > b > 0 , let the (1) eccentricity of E be reciprocal of the eccentricity of H , and (2)

JEE Main 2022 Solution View → 50

A common tangent T to the curves C _ 1 : x ^ 2 4 + y ^ 2 9 = 1 and C _ 2 : x ^ 2 42 - y ^ 2 143 = 1 does not pass through the fourth quadrant. If T touches C _ 1 at ( x _ 1 , y _

JEE Main 2022 Solution View → 51

An ellipse E: x ^ 2 a ^ 2 + y ^ 2 b ^ 2 = 1 passes through the vertices of the hyperbola H: x ^ 2 49 - y ^ 2 64 = - 1 . Let the major and minor axes of the ellipse E coincide with

JEE Main 2022 Solution View → 52

If the line x - 1 = 0 , is a directrix of the hyperbola k x ^ 2 - y ^ 2 = 6 , then the hyperbola passes through the point

JEE Main 2022 Solution View → 53

Let the tangent drawn to the parabola y ^ 2 = 24x at the point (α, β) is perpendicular to the line 2x + 2y = 5 . Then the normal to the hyperbola x ^ 2 α ^ 2 - y ^ 2 β ^ 2 = 1 at

JEE Main 2022 Solution View → 54

Let the foci of the ellipse x ^ 2 16 + y ^ 2 7 = 1 and the hyperbola x ^ 2 144 - y ^ 2 α = (1)/(25) coincide. Then the length of the latus rectum of the hyperbola is:

JEE Main 2022 Solution View → 55

Let the equation of two diameters of a circle x ^ 2 + y ^ 2 - 2x + 2fy + 1 = 0 be 2px - y = 1 and 2x + py = 4p . Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3 x ^ 2

JEE Main 2022 Solution View → 56

Let H: x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1, a > 0, b > 0 , be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4(2 2 + 14 ) . If the eccentricity H

JEE Main 2022 Solution View → 57

Let a > 0, b > 0 . Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 . Let e ^ ' and l ^ ' respectively

JEE Main 2022 Solution View → 58

Let the eccentricity of the hyperbola H: x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 be (5)/(2) and length of its latus rectum be 6 2 . If y = 2x + c is a tangent to the hyperbola H , then the

JEE Main 2022 Solution View → 59

The normal to the hyperbola x ^ 2 a ^ 2 - y ^ 2 9 = 1 at the point (8, 3 3 ) on it passes through the point

JEE Main 2022 Solution View → 60

Let a line L _ 1 be tangent to the hyperbola x ^ 2 16 - y ^ 2 4 = 1 and let L _ 2 be the line passing through the origin and perpendicular to L _ 1 . If the locus of the point of

JEE Main 2022 Solution View → 61

Let the eccentricity of the hyperbola x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 be (5)/(4) . If the equation of the normal at the point ( 8 5 , (12)/(5)) on the hyperbola is 8 5 x + = λ

JEE Main 2022 Solution View → 62

Let the hyperbola H: x ^ 2 a ^ 2 - y ^ 2 = 1 and the ellipse E: 3 x ^ 2 + 4 y ^ 2 = 12 be such that the length of latus rectum of H is equal to the length of latus rectum of E .

JEE Main 2022 Solution View → 63

Let - 2y = μ be a tangent to the hyperbola a ^ 2 x ^ 2 - y ^ 2 = b ^ 2 . Then ((λ)/(a)) ^ 2 - ((μ)/(b)) ^ 2 is equal to

JEE Main 2022 Solution View → 64

Let P(asecθ, btanθ) and Q(asecϕ, btanϕ) where θ + ϕ = (π)/(2), be two points on the hyperbola x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 . If the ordinate of the point of intersection of

JEE Main 2021 Solution View → 65

The point P ( - 2 6 , 3 ) lies on the hyperbola x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 having eccentricity 5 2 . If the tangent and normal at P to the hyperbola intersect its conjugate

JEE Main 2021 Solution View → 66

The locus of the mid points of the chords of the hyperbola x ^ 2 - y ^ 2 = 4, which touch the parabola y ^ 2 = 8x, is :

JEE Main 2021 Solution View → 67

The locus of the centroid of the triangle formed by any point P on the hyperbola 16 x ^ 2 - 9 y ^ 2 + 32x + 36y - 164 = 0 and its foci is

JEE Main 2021 Solution View → 68

Let a line L: 2x + y = k, k > 0 be a tangent to the hyperbola x ^ 2 - y ^ 2 = 3 . If L is also a tangent to the parabola y ^ 2 = , then α is equal to:

JEE Main 2021 Solution View → 69

Consider a hyperbola H: x^ 2 - 2y^ 2 = 4 . Let the tangent at a point P ( 4, 6 ) meet the x -axis at Q and latus rectum at R( x _ 1 , y _ 1 ), x _ 1 > 0 . If F is a focus of H

JEE Main 2021 Solution View → 70

A square ABCD has all its vertices on the curve x ^ 2 y ^ 2 = 1 . The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is

JEE Main 2021 Solution View → 71

The locus of the midpoints of the chord of the circle, x ^ 2 + y ^ 2 = 25 which is tangent to the hyperbola, x ^ 2 9 - y ^ 2 16 = 1 is :

JEE Main 2021 Solution View → 72

A hyperbola passes through the foci of the ellipse x ^ 2 25 + y ^ 2 16 = 1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively.

JEE Main 2021 Solution View → 73

The locus of the point of intersection of the lines ( 3 )kx + ky - 4 3 = 0 and 3 x - y - 4( 3 )k = 0 is a conic, whose eccentricity is

JEE Main 2021 Solution View → 74

Let a and b be positive real numbers such that a > 1 and b < a . Let P be a point in the first quadrant that lies on the hyperbola x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 . Suppose the

JEE Advanced 2020 Solution View → 75

If the line y = mx + c is a common tangent to the hyperbola x ^ 2 100 - y ^ 2 64 = 1 and the circle x ^ 2 + y ^ 2 = 36, then which one of the following is true?

JEE Main 2020 Solution View → 76

Let P(3, 3) be a point on the hyperbola, x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 . If the normal to it at P intersects the x -axis at (9, 0) and e is its eccentricity, then the ordered pair

JEE Main 2020 Solution View → 77

Let e _ 1 and e _ 2 be the eccentricities of the ellipse x ^ 2 25 + y ^ 2 b ^ 2 = 1(b < 5) and the hyperbola x ^ 2 16 - y ^ 2 b ^ 2 = 1 respectively satisfying e _ 1 e _ 2 = 1 .

JEE Main 2020 Solution View → 78

A hyperbola having the transverse axis of length, 2 has the same foci as that of the ellipse, 3 x ^ 2 + 4 y ^ 2 = 12 then this hyperbola does not pass through which of the

JEE Main 2020 Solution View → 79

For some θ ∈ (0, (π)/(2)), if the eccentricity of the hyperbola, x ^ 2 - y ^ 2 sec ^ 2 θ = 10 is 5 times the eccentricity of the ellipse, x ^ 2 sec ^ 2 θ + y ^ 2 = 5, then the

JEE Main 2020 Solution View → 80

A line parallel to the straight line 2x - y = 0 is tangent to the hyperbola x ^ 2 4 - y ^ 2 2 = 1 at the point ( x _ 1 , y _ 1 ) . Then x _ 1 ^ 2 + 5 y _ 1 ^ 2 is equal to

JEE Main 2020 Solution View → 81

If e _ 1 and e _ 2 are the eccentricities of the ellipse x ^ 2 18 + y ^ 2 4 = 1 and the hyperbola x ^ 2 9 - y ^ 2 4 = 1 respectively and ( e _ 1 , e _ 2 ) is a point on the

JEE Main 2020 Solution View → 82

If a hyperbola passes through the point P(10, 16), and it has vertices at (± 6, 0), then the equation of the normal to it at P , is.

JEE Main 2020 Solution View → 83

Number of points from where perpendicular tangents to the curve x^ 2 16 - y^ 2 25 = 1 can be drawn, is/are

NTA Abhyas JEE Main 2020 Solution View → 84

Tangents are drawn from the point (α, β) to the hyperbola 3 x ^ 2 - 2 y ^ 2 = 6 and are inclined at angles θ and ϕ to the x -axis. If (tan ⁡ θ)(tan ⁡ ϕ) = 2 , then the value of 2

NTA Abhyas JEE Main 2020 Solution View → 85

The equation of a hyperbola is x^ 2 a^ 2 - y^ 2 b^ 2 = 1 . If P ( 2 , 5 ) is a point from which perpendicular tangents can be drawn to the hyperbola and distance between both the

NTA Abhyas JEE Main 2020 Solution View → 86

Let x ^ 2 + y ^ 2 = 4 r ^ 2 and xy = 1 intersects at A and B in first quadrant. If AB = 14 units, then the value of |r| is

NTA Abhyas JEE Main 2020 Solution View → 87

If two points P and Q lie on the hyperbola (x2)/(a2) - (y2)/(b2) = 1 ( a < b ) , whose centre C be such that CP is perpendicular to CQ , then the value of 1 CP^ 2 + 1 CQ^ 2 is

NTA Abhyas JEE Main 2020 Solution View → 88

If a circle drawn by assuming a chord parallel to the transverse axis of hyperbola x^ 2 a^ 2 - y^ 2 b^ 2 = 1 as diameter always passes through (2,0) , then

NTA Abhyas JEE Main 2020 Solution View → 89

If the focus of a hyperbola is ( ± 3,0 ) and the equation of a tangent is 2x + y - 4 = 0 , then the equation of the hyperbola is

NTA Abhyas JEE Main 2020 Solution View → 90

From a point P, two tangents PA and PB are drawn to the hyperbola x^ 2 a^ 2 - y^ 2 b^ 2 = 1 . If these tangents cut the coordinate axes at 4 concyclic points, then the locus of P

NTA Abhyas JEE Main 2020 Solution View → 91

For the hyperbola x^ 2 a^ 2 - y^ 2 b^ 2 = 1, distance between the foci is 10 ~units. From the point (2, 3 ), perpendicular tangents are drawn to the hyperbola, then the value of

NTA Abhyas JEE Main 2020 Solution View → 92

A tangent drawn to the hyperbola x^ 2 a^ 2 - y^ 2 b^ 2 = 1 at P ( asec ⁡ (π)/(6), btan ⁡ (π)/(6)) form a triangle of area 3a^ 2 sq. units with the coordinate axes. The

NTA Abhyas JEE Main 2020 Solution View → 93

The locus of the mid-point of the chords of the hyperbola x^ 2 - y^ 2 = 4, that touches the parabola y^ 2 = 8x is

NTA Abhyas JEE Main 2020 Solution View → 94

The locus of the mid-points of the chords of the hyperbola 3x^ 2 - 2y^ 2 + 4x - 6y = 0 which are parallel to the line y = 2x + 4 & is

NTA Abhyas JEE Main 2020 Solution View → 95

The chords passing through (2,1) intersect the hyperbola x^ 2 16 - y^ 2 9 = 1 at A and B . The locus of the point of intersection of tangents at A and B on the hyperbola is

NTA Abhyas JEE Main 2020 Solution View → 96

Two straight lines having variable slopes m _ 1 ~and& m _ 2 pass through the fixed points~ (a, 0) ~and& (- a, 0) respectively. If m _ 1 m _ 2 = 2 , then the eccentricity of the

NTA Abhyas JEE Main 2020 Solution View → 97

The sum of the y -intercepts of the tangents drawn from the point (- 2, - 1) to the hyperbola x ^ 2 3 - y ^ 2 2 = 1 is

NTA Abhyas JEE Main 2020 Solution View → 98

The locus of a point which moves such that the difference of its distances from the points (5,0) and (- 5,0) is 6 & units is a conic, whose length of the latus rectum (in units)

NTA Abhyas JEE Main 2020 Solution View → 99

If the line y = x + c touches the hyperbola x^ 2 9 - y^ 2 5 = 1 at the point P (h, k), then (h, k) can be equal to

NTA Abhyas JEE Main 2020 Solution View → 100

The area (in sq. units) of the triangle formed by the lines y = 2x, y = - 2x and the tangent at the point ( 5 , 4) on 4x^ 2 - y^ 2 = 4 is equal to

NTA Abhyas JEE Main 2020 Solution View → 101

Let the eccentricity of the hyperbola with the principal axes along the coordinate axes and passing through (3,0) and (3 2 , 2) is e , then the value of ( e ^ 2 + 1 e ^ 2 - 1 ) is

NTA Abhyas JEE Main 2020 Solution View → 102

The point of intersection of the tangents drawn to the hyperbola x^ 2 a^ 2 - y^ 2 b^ 2 = 1 at the points where it is intersected by the line lx + my + n = 0 is&

NTA Abhyas JEE Main 2020 Solution View → 103

The locus of the mid-points of the parallel chords with slope m of the rectangular hyperbola xy = c^ 2 is

NTA Abhyas JEE Main 2020 Solution View → 104

Values of m , for which the line y = mx + 2 5 is a tangent to the hyperbola 16 x ^ 2 - 9 y ^ 2 = 144 , are the roots of the equation x ^ 2 - (a + b)x - 4 = 0, then the value of (a

NTA Abhyas JEE Main 2020 Solution View → 105

The locus of the point of intersection of two tangents of the hyperbola x^ 2 2 - y^ 2 4 = 1, if the product of their slopes is 1, & is

NTA Abhyas JEE Main 2020 Solution View → 106

If e _ 1 and e _ 2 are the eccentricities of the ellipse~ x^ 2 18 + y^ 2 4 = 1 and the hyperbola x^ 2 9 - y^ 2 4 = 1 respectively and ( e _ 1 , e _ 2 ) is a point on the ellipse~

NTA Abhyas JEE Main 2020 Solution View → 107

If the eccentricity of the hyperbola x^ 2 - y^ 2 ^ 2 ⁡ α = 5 is 3 times the eccentricity of the ellipse x^ 2 ^ 2 ⁡ α + y^ 2 = 25, then ^ 2 ⁡ α is equal to

NTA Abhyas JEE Main 2020 Solution View → 108

The area of triangle formed by the lines x - y = 0, x + y = 0 and any tangent to the hyperbola x^ 2 - y^ 2 = 16 is equal to

NTA Abhyas JEE Main 2020 Solution View → 109

The locus of a point P (α, β) moving under the condition that the line y = + β is a tangent to the hyperbola x^ 2 1 - y^ 2 b^ 2 =1 is a conic, with eccentricity equal to

NTA Abhyas JEE Main 2020 Solution View → 110

From a point on the line x - y + 2 = 0 tangents are drawn to the hyperbola x^ 2 6 - y^ 2 2 = 1 such that the chord of contact passes through a fixed point (λ, μ) . Then,~ μ - λ is

NTA Abhyas JEE Main 2020 Solution View → 111

From a point P, two tangents PA and PB are drawn to the hyperbola x^ 2 a^ 2 - y^ 2 b^ 2 = 1 . If the product of the slopes of these tangents is 1, then the locus of P is a conic

NTA Abhyas JEE Main 2020 Solution View → 112

A hyperbola has foci (4,2), (2, 2) and it passes throughP (2, 4) . & The eccentricity of the hyperbola is

NTA Abhyas JEE Main 2020 Solution View → 113

The locus of the midpoint of the chords of the hyperbola (x2)/(25) - (y2)/(36) = 1 which passes through the point (2, 4) is a hyperbola, whose transverse axis length (in units) is

NTA Abhyas JEE Main 2020 Solution View → 114

A hyperbola having the transverse axis of length 2 units has the same focii as that of ellipse 3x^ 2 + 4y^ 2 = 12 , then its equation is

NTA Abhyas JEE Main 2020 Solution View → 115

Let C _ 1 be the graph of xy = 1 and the reflection of C _ 1 in the line y = 2x is C _ 2 . If the equation of C _ 2 is expressed as 12 x ^ 2 + bxy + c y ^ 2 + d = 0 , then the

NTA Abhyas JEE Main 2020 Solution View → 116

The area (in sq. units) of the triangle formed by the latus rectum and the tangents at the end points of the latus rectum of x ^ 2 16 - y ^ 2 9 = 1 is equal to

NTA Abhyas JEE Main 2020 Solution View → 117

If the eccentricity of the hyperbola x^ 2 (1 + sin ⁡ θ) ^ 2 - y^ 2 ^ 2 ⁡ θ = 1 is 2 3 , then the sum of all the possible values of θ is (where, θ ∈ (0, π))

NTA Abhyas JEE Main 2020 Solution View → 118

From a point P, tangents are drawn to the curve x ^ 2 2 - y ^ 2 = 1 . If the chord of contact is a normal chord and the locus of P is the curve 8 x ^ 2 - 1 y ^ 2 = 10λ, then the

NTA Abhyas JEE Main 2020 Solution View → 119

The tangent drawn to the hyperbola x^ 2 16 - y^ 2 9 = 1, at point P in the first quadrant whose abscissa is 5, meets the lines 3x - 4y = 0 and 3x + 4y = 0 at Q and R respectively.

NTA Abhyas JEE Main 2020 Solution View → 120

Let the variable line y = kx + h is tangent to the hyperbola x^ 2 4 - y^ 2 9 = 1 . If the locus of P (h, k) is a conic, then which of the following statement is false about this

NTA Abhyas JEE Main 2020 Solution View → 121

If the line 2x + 6 y = 2 touches the hyperbola x ^ 2 - 2 y ^ 2 = a ^ 2 , then a ^ 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 122

If the eccentricity of the hyperbola x^ 2 16 - y^ 2 b^ 2 = - 1 is (5)/(4), then b^ 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 123

The equation of a common tangent to the curves, y ^ 2 = 16x and xy = - 4, is:

JEE Main 2019 Solution View → 124

Let P be the point of intersection of the common tangents to the parabola y ^ 2 = 12x and the hyperbola 8 x ^ 2 - y ^ 2 = 8 . If S and S ^ ' denote the foci of the hyperbola where

JEE Main 2019 Solution View → 125

If 5x + 9 = 0 is the directrix of the hyperbola 16 x ^ 2 - 9 y ^ 2 = 144, then its corresponding focus is:

JEE Main 2019 Solution View → 126

If a directrix of a hyperbola centered at the origin and passing through the point (4, - 2 3 ) is 5x = 4 5 and its eccentricity is e , then:

JEE Main 2019 Solution View → 127

If the line y = mx + 7 3 is normal to the hyperbola x ^ 2 24 - y ^ 2 18 = 1 , then a value of m is:

JEE Main 2019 Solution View → 128

If the eccentricity of the standard hyperbola passing through the point ( 4,6 ) is 2, then the equation of the tangent to the hyperbola at ( 4,6 ) is:

JEE Main 2019 Solution View → 129

If the vertices of a hyperbola be at (- 2, 0) and (2, 0) and one of its foci be at (- 3, 0) , then which one of the following points does not lie on this hyperbola ?

JEE Main 2019 Solution View → 130

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 , then the eccentricity of the hyperbola is:

JEE Main 2019 Solution View → 131

Equation of a common tangent to the parabola y^ 2 =4 x and the hyperbola x y=2 is :

JEE Main 2019 Solution View → 132

The equation of a tangent to the hyperbola, 4 x ^ 2 - 5 y ^ 2 = 20, parallel to the line x - y = 2, is

JEE Main 2019 Solution View → 133

A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x - axis . Then the eccentricity of the hyperbola is:

JEE Main 2019 Solution View → 134

Let 0 < θ < (π)/(2) . If the eccentricity of the hyperbola x ^ 2 ^ 2 ⁡ θ - y ^ 2 ^ 2 ⁡ θ = 1 is greater than 2, then the length of its latus rectum lies in the interval:

JEE Main 2019 Solution View → 135

Let H: x ^ 2 a ^ 2 - y ^ 2 b ^ 2 = 1 , where a > b > 0 , be a hyperbola in the xy-plane whose conjugate axis LM subtends an angle of 60 ^ o at one of its vertices N . Let the area

JEE Advanced 2018 Solution View → 136

A normal to the hyperbola, 4 x^2-9 y^2=36 meets the co-ordinate axes x and y at A and B , respectively. If the parallelogram O A B P(O being the origin) is formed, then the locus

JEE Main 2018 Solution View → 137

If the tangents drawn to the hyperbola 4 y^2=x^2+ 1 intersect the co-ordinate axes at the distinct points A and B , then the locus of the mid point of A B is

JEE Main 2018 Solution View → 138

If the tangent drawn to the hyperbola 4 y ^ 2 = x ^ 2 + 1 intersect the co-ordinates axes at the distinct points A and B , then the locus of the midpoint of AB is :

JEE Main 2018 Solution View → 139

Tangents are drawn to the hyperbola 4 x ^ 2 - y ^ 2 = 36 at the points P and Q . If these tangents intersect at the point T(0, 3) then the area (in sq. units) of is:

JEE Main 2018 Solution View → 140

If 2x - y + 1 = 0 is a tangent to the hyperbola x ^ 2 a ^ 2 - y ^ 2 16 = 1 , then which of the following CANNOT be sides of a right angled triangle?

JEE Advanced 2017 Solution View → 141

A hyperbola passes through the point P( 2 , 3 ) and has foci at (± 2, 0). Then the tangent to this hyperbola at P also passes through the point

JEE Main 2017 Solution View → 142

A hyperbola whose transverse axis is along the major axis of the conic x ^ 2 3 + y ^ 2 4 = 4 and has vertices at the foci of the conic. If the eccentricity of the hyperbola is

JEE Main 2016 Solution View → 143

Let a and b respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation 9 e ^ 2 - 18e + 5 = 0 . If S(5, 0) is a

JEE Main 2016 Solution View → 144

The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is

JEE Main 2016 Solution View → 145

Consider the hyperbola H: x ^ 2 - y ^ 2 = 1 and a circle S with center N( x _ 2 , 0) . Suppose that H and S touch each other at point P( x _ 1 , y _ 1 ) with x _ 1 > 1and y _ 1 >

JEE Advanced 2015 Solution View → 146

The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola x ⁡ ^ 2 4 - y ⁡ ^ 2 5 = 1 , meets the x -axis and y -axis at A and B , respectively. Then

JEE Main 2014 Solution View → 147

Let P(3 θ, 2 θ) and Q(3 φ, 2 φ) where θ+φ=(π)/(2) , be two distinct points on the hyperbola (x^2)/(9)-(y^2)/(4)=1 . Then the ordinate of the point of intersection of the normals

JEE Main 2014 Solution View → 148

Consider the system of equations : x+a y=0, y+a z=0 and z+a x=0 . Then the set of all real values of ' a ' for which the system has a unique solution is:

JEE Main 2013 Solution View → 149

A tangent to the hyperbola (x^2)/(4)-(y^2)/(2)=1 meets x -axis at P and y -axis at Q . Lines PR and QR are drawn such that OPRQ is a rectangle (where O is the origin). Then R lies

JEE Main 2013 Solution View → 150

Tangents are drawn to the hyperbola x^ 2 9 - y^ 2 4 =1 , parallel to the straight line 2 x-y=1 . The points of contact of the tangents on the hyperbola are

JEE Advanced 2012 Solution View → 151

If the eccentricity of a hyperbola (x^2)/(9)-(y^2)/(b^2)=1 , which passes through (K, 2) , is 13 3 , then the value of K^2 is

JEE Main 2012 Solution View → 152

Let P(6,3) be a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the normal at the point P intersects the X -axis at (9,0) , then the eccentricity of the hyperbola is

JEE Advanced 2011 Solution View → 153

Let the eccentricity of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 be reciprocal to that of the ellipse x^2+4 y^2=4 . If the hyperbola passes through a focus of the ellipse, then

JEE Advanced 2011 Solution View → 154

Paragraph: The circle x^2+y^2-8 x=0 and hyperbola (x^2)/(9)-(y^2)/(4)=1 intersect at the points A and B . Question: Equation of a common tangent with positive slope to the circle

JEE Advanced 2010 Solution View → 155

The line 2 x+y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If this line passes through the point of intersection of the nearest directrix and the x -axis, then the

JEE Advanced 2010 Solution View → 156

Match the conics in Column I with the statements/expressions in Column II.

JEE Advanced 2009 Solution View → 157

Consider a branch of the hyperbola x^2-2 y^2-2 2 x-4 2 y-6=0 with vertex at the point A . Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola

JEE Advanced 2008 Solution View → 158

For the hyperbola (x^2)/( ^2 α)-(y^2)/( ^2 α)=1 , which of the following remains constant when α varies?

JEE Main 2007 Solution View → 159

If e_1 is the eccentricity of the ellipse (x^2)/(16)+(y^2)/(25)=1 and e_2 is the eccentricity of the hyperbola passing through the focii of the ellipse and e_1 e_2=1 , then

JEE Advanced 2006 Solution View → 160

The locus of a point P(α, β) moving under the condition that the line y=α x+β is a tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is

JEE Main 2005 Solution View → 161

The equation of the directrices of the hyperbola 3 x^ 2 -3 y^ 2 -18 x+12 y+2=0 is

Highly selective Backlog Qs for JEE Main Solution View → 162

If the eccentricity of the hyperbola x^ 2 -y^ 2 cosec^ 2 α=25 is 5 times the eccentricity of the ellipse x^ 2 cosec^ 2 α+y^ 2 =5 then α is equal to :

Highly selective Backlog Qs for JEE Main Solution View → 163

A point moves in such a way that the difference of its distance from two points (8,0) and (-8,0) always remains 4 . Then, the locus of the point is

Highly selective Backlog Qs for JEE Main Solution View → 164

The eccentricity of a rectangular hyperbola is

Highly selective Backlog Qs for JEE Main Solution View → 165

The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is

Highly selective Backlog Qs for JEE Main Solution View → 166

A double ordinate PQ of the hyperbola ^ 2 ^ 2 - ^ 2 ~b^ 2 =1 is such that Δ OPQ is equilateral, O being the centre of the hyperbola. Then the eccentricity e satisfies the relation

Highly selective Backlog Qs for JEE Main Solution View → 167

The distance between the foci of the hyperbola x^2-3 y^2-4 x-6 y-11=0 is

Highly selective Backlog Qs for JEE Main Solution View → 168

A hyperbola passing through a focus of the ellipse (x^2)/(169)+(y^2)/(25)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse.

Highly selective Backlog Qs for JEE Main Solution View → 169

The distance between the foci of the hyperbola x^2-3 y^2-4 x-6 y-11=0 is

Highly selective Backlog Qs for JEE Main Solution View → 170

If the focii of the ellipse (x^2)/(25)+(y^2)/(16)=1 and the hyperbola (x^2)/(4)-(y^2)/(b^2)=1 coincide, then b^2 is equal to

Highly selective Backlog Qs for JEE Main Solution View → 171

The equation | x^ 2 + (y - 1) ^ 2 - x^ 2 + (y + 1) ^ 2 | = K will represent a hyperbola for -

Highly selective Backlog Qs for JEE Main Solution View → 172

For the hyperbola x^2-y^2-4 x+2 y+c=0 , if the focus is S(2+2 2 , k) and the directrix that is adjacent to S is x=2+ 2 , then c=

Highly selective Backlog Qs for JEE Main Solution View → 173

If e_1 is the eccentricity of the ellipse (x^2)/(16)+(y^2)/(25)=1 and e_2 is the eccentricity of a hyperbola passing through the foci of the given ellipse and e_1 e_2=1 , then the

Highly selective Backlog Qs for JEE Main Solution View → 174

The equation of the hyperbola having eccentricity 2 ,~such that the distance between its foci is 8 ~and the major axis is along the x -axis, while the minor axis is along the y

Highly selective Backlog Qs for JEE Main Solution View → 175

A hyperbola having its centre at the origin is passing through the point (5,2) and has transverse axis of length 8 along the X -axis. Then the eccentricity of its conjugate

Highly selective Backlog Qs for JEE Main Solution View → 176

Let P((π)/(4)), Q \ left((5 π)/(4)), R\ left((3 π)/(4)), T\ left((7 π)/(4)) be the points on the hyperbola x^2-4 y^2-4=0 in the parametric form. Then the area of the quadrilateral

Highly selective Backlog Qs for JEE Main Solution View → 177

If two points P and Q lie on the hyperbola (x2)/(a2) - (y2)/(b2) = 1 ( a < b ) , whose centre C be such that CP is perpendicular to CQ , then the value of 1 CP^ 2 + 1 CQ^ 2 is

Highly selective Backlog Qs for JEE Main Solution View → 178

If a directrix of a hyperbola centered at the origin and passing through the point (4, - 2 3 ) is 5x = 4 5 ~and~its eccentricity is e , then:

Highly selective Backlog Qs for JEE Main Solution View → 179

Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements is -3 . If the points (x, y) satisfying A^2+x ~A+y I=O lie on a hyperbola, whose length of

Highly selective Backlog Qs for JEE Main Solution View → 180

Let & LL^ &#39; be the latus rectum through the focus S of a hyperbola and A ~be the farther vertex of the conic. If Δ ALL^ &#39; is equilateral then its eccentricity is

Highly selective Backlog Qs for JEE Main Solution View → 181

If the focus of a hyperbola is ( ± 3,0 ) and the equation of a tangent is 2x + y - 4 = 0 , then the equation of the hyperbola is

99 Percentile Qs Bank for JEE Main Solution View → 182

If m is a variable, the locus of the point of intersection of the lines& x 3 - y 2 = m and x 3 + y 2 = 1 m is a/an :

99 Percentile Qs Bank for JEE Main Solution View → 183

Two straight lines having variable slopes m _ 1 and m _ 2 pass through the fixed points (a, 0) and (- a, 0) respectively. If m _ 1 m _ 2 = 2 , then the eccentricity of the locus

99 Percentile Qs Bank for JEE Main Solution View → 184

If the focii of the ellipse (x^2)/(25)+(y^2)/(16)=1 and the hyperbola (x^2)/(4)-(y^2)/(b^2)=1 coincide, then b^2 is equal to

99 Percentile Qs Bank for JEE Main Solution View → 185

If x=9 is a chord of contact of the hyperbola x^2-y^2=9 , then the equation of the tangent at one of the points of contact is

99 Percentile Qs Bank for JEE Main Solution View → 186

A hyperbola passing through a focus of the ellipse (x^2)/(169)+(y^2)/(25)=1 . Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse.

99 Percentile Qs Bank for JEE Main Solution View → 187

The mid point of the chord 4 x-3 y=5 of the hyperbola 2 x^2-3 y^2=12 is

99 Percentile Qs Bank for JEE Main Solution View → 188

The equation of the hyperbola with vertices (3, 0), (-3, 0) and semi-latus rectum 4 is given by:

99 Percentile Qs Bank for JEE Main Solution View → 189

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 in four points (x_i, y_i) , for i=1,2,3 and 4 , then y_1+y_2+y_3+y_4 equals

99 Percentile Qs Bank for JEE Main Solution View → 190

If e _ 1 and e _ 2 are the eccentricities of the ellipse x^ 2 18 + y^ 2 4 = 1 and the hyperbola x^ 2 9 - y^ 2 4 = 1 respectively and ( e _ 1 , e _ 2 ) is a point on the ellipse

99 Percentile Qs Bank for JEE Main Solution View → 191

For the hyperbola x^2-y^2-4 x+2 y+c=0 , if the focus is S(2+2 2 , k) and the directrix that is adjacent to S is x=2+ 2 , then c=

99 Percentile Qs Bank for JEE Main Solution View → 192

If the latus rectum of a hyperbola (x2)/(a2) - (y2)/(b2) = 1 subtends an angle of 60 ° at the other focus, then the eccentricity of the hyperbola is

99 Percentile Qs Bank for JEE Main Solution View → 193

The line 2 x+y=1 is a tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1(a>b) . If this line passes through the point of intersection of a directrix and the positive X -axis, then

99 Percentile Qs Bank for JEE Main Solution View → 194

Let A ( &#952; _ 1 ) ~and B ( &#952; _ 2 )~be two points on the hyperbola (x2)/(a2) - (y2)/(b2) =1 ~and S ~be the focus of the hyperbola. If A, S, B ~are collinear and acos (

99 Percentile Qs Bank for JEE Main Solution View → 195

The locus of a point which moves such that the difference of its distances from the points (5,0) and (- 5,0) is 6 units is a conic, whose length of the latus rectum (in units) is

99 Percentile Qs Bank for JEE Main Solution View → 196

The equation& of the chord of the hyperbola 25x^ 2 - 16y^ 2 = 400 , which is bisected at the point ( 6, 2 ) , is

99 Percentile Qs Bank for JEE Main Solution View → 197

If P ( x _ 1 , y _ 1 ) is a point on the hyperbola x^ 2 - y^ 2 = a^ 2 , then SP . S^ ' P = ________

99 Percentile Qs Bank for JEE Main Solution View → 198

If two points P and Q lie on the hyperbola (x2)/(a2) - (y2)/(b2) = 1 ( a < b ) , whose centre C be such that CP is perpendicular to CQ , then the value of 1 CP^ 2 + 1 CQ^ 2 is

99 Percentile Qs Bank for JEE Main Solution View → 199

If e_1 is the eccentricity of the hyperbola x= θ , y= 2 θ and e_2 is the eccentricity of the hyperbola x= 2 θ, y= θ , then (e_2^2)/(e_1^2)=

99 Percentile Qs Bank for JEE Main Solution View → 200

The locus of a point which is at a distance of 2 units from the line 2 x-3 y+4=0 and at a distance of 13 units from a point (5,0) is

99 Percentile Qs Bank for JEE Main Solution View →
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Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Hyperbola in other exams

NDA Hyperbola (13)BITSAT Hyperbola (7)