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Hyperbola — JEE Main & Advanced Mathematics PYQs

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

276 questionsMathematicsSolutions on every page
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 hyperbola x^2 b^

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= intersects the hyperbola H

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 triangl

JEE Main 2026 Solution View → 5

For some (0, 2 ) , let the eccentricity and the length of the latus rectum of the hyperbola x²-y² ² =8 be e₁ and l₁ , respectively, and let the eccentricity and the length of the l

JEE Main 2026 Solution View → 6

Let PQ be a chord of the hyperbola x² 4 - y² b² =1 , perpendicular to the x -axis such that OPQ is an equilateral triangle, O being the centre of the hyperbola. If the eccentricity

JEE Main 2026 Solution View → 7

Let the domain of the function f(x)= ₃ ₅ ₇ (9 x-x²-13 ) be the interval ( m , n ) . Let the hyperbola x² a ² - y² ~b ² =1 have eccentricity n 3 and the length of the latus rectum 8

JEE Main 2026 Solution View → 8

Let P (10,2 15 ) be a point on the hyperbola x² a ² - y² ~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 PSS ^ is equal

JEE Main 2026 Solution View → 9

If the line x+2 y=1 , where R , does not meet the hyperbola x²-9 y²=9 , then a possible value of is:

JEE Main 2026 Solution View → 10

Let the foci of a hyperbola coincide with the foci of the ellipse x² 36 + y² 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 e₁ and e₂ 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= 2 - , , N .

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- x+ y+ =0 , then + + 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

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 leng

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 PAB lies

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 e₁= 5 2

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 x^2 ^2 - y^

JEE Main 2025 Solution View → 21

Let E : x^2 a ^2 + y^2 ~b ^2 =1, a b 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 eccentrici

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 eccentricity of

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 the orig

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 ( , 6), >0 lies on H . If is the product of 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 (x₀, y₀ ) . If

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 circl

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

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 2 b 2 = 1 i

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 is:

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 smaller

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 hyperbola x 2

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 the d

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 are co-prime numb

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 foci of the hype

JEE Main 2024 Solution View → 36

The foci of a hyperbola are ( &#177; 2 , 0 ) and its eccentricity is 3 2 . A tangent, perpendicular to the line 2 x + 3 y = 6 , is drawn at a point in the first quadrant on the hyp

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 have slopes

JEE Main 2023 Solution View → 38

Let the tangent to the parabola y 2 = 12 x at the point 3 , &#945; be perpendicular to the line 2 x + 2 y = 3 . Then the square of distance of the point 6 , - 4 from the normal to

JEE Main 2023 Solution View → 39

Let H n : x 2 1 + n - y 2 3 + n = 1 , n &#8712; &#8469; . 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 la

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 &#945; , 0 and B 0 , &#946; , &#945; &#8712; 0 , 2 and &#946; &#8712; 0 , 5 , be such that the line

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 angles, then sq

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 3 x + 2 y = 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 &#177; 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 &#60; 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 &#177; 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

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 &#8736; S P

JEE Advanced 2022 Solution View → 47

Let the focal chord of the parabola P : y 2 = 4 x along the line L : y = m x + c , m &#62; 0 meet the parabola at the points M and N . Let the line L be a tangent to the hyperbola

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 directrix

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 &#62; b &#62; 0 , let the (1) eccentricity of E be reciprocal of the eccentricity of H , and (2) t

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 1 and C 2 at x 2 , 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 the transv

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 = 24 x at the point &#945; , &#946; is perpendicular to the line 2 x + 2 y = 5 . Then the normal to the hyperbola x 2 &#945; 2 - y 2 &#946

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 &#945; = 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 - 2 x + 2 f y + 1 = 0 be 2 p x - y = 1 and 2 x + p y = 4 p . Then the slope m &#8712; 0 , &#8734; of the tangent to the hype

JEE Main 2022 Solution View → 56

Let H : x 2 a 2 - y 2 b 2 = 1 , a &#62; 0 , b &#62; 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 i

JEE Main 2022 Solution View → 57

Let a &#62; 0 , b &#62; 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 the ec

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 = 2 x + c is a tangent to the hyperbola H , then the value of c

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 intersectio

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 + &#946; y = &#955; , then &#95

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 . If e H and

JEE Main 2022 Solution View → 63

Let &#955; x - 2 y = &#956; be a tangent to the hyperbola a 2 x 2 - y 2 = b 2 . Then &#955; a 2 - &#956; b 2 is equal to

JEE Main 2022 Solution View → 64

Let P a sec &#952; , b tan &#952; and Q a sec &#981; , b tan &#981; where &#952; + &#981; = &#960; 2 , be two points on the hyperbola x 2 a 2 - y 2 b 2 = 1 . If the ordinate of the

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 axis at the

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 = 8 x , 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 + 32 x + 36 y - 164 = 0 and its foci is

JEE Main 2021 Solution View → 68

Let a line L : 2 x + y = k , k &#62; 0 be a tangent to the hyperbola x 2 - y 2 = 3 . If L is also a tangent to the parabola y 2 = &#945; x , then &#945; is equal to:

JEE Main 2021 Solution View → 69

Consider a hyperbola H : x 2 - 2 y 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 &#62; 0 . If F is a focus of H which i

JEE Main 2021 Solution View → 70

A square A B C D 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 A B C D 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. If the

JEE Main 2021 Solution View → 73

The locus of the point of intersection of the lines 3 k x + k y - 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 &#62; 1 and b &#60; 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 tange

JEE Advanced 2020 Solution View → 75

If the line y = m x + 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 a 2 , e 2

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 &#60; 5 and the hyperbola x 2 16 - y 2 b 2 = 1 respectively satisfying e 1 e 2 = 1 . If &#945; and &#946

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 following po

JEE Main 2020 Solution View → 79

For some &#952; &#8712; 0 , &#960; 2 , if the eccentricity of the hyperbola, x 2 - y 2 sec 2 &#952; = 10 is 5 times the eccentricity of the ellipse, x 2 sec 2 &#952; + y 2 = 5 , th

JEE Main 2020 Solution View → 80

A line parallel to the straight line 2 x - y = 0 is tangent to the hyperbola x 2 4 &#8722; 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 ellipse 15 x 2 + 3 y 2 = k

JEE Main 2020 Solution View → 82

If a hyperbola passes through the point P 10 , &#8201; 16 , and it has vertices at &#177; 6 , &#8201; 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 &#945; , &#160; &#946; to the hyperbola 3 x 2 - 2 y 2 = 6 and are inclined at angles &#952; and &#981; to the x -axis. If tan &#8289; &#952; tan &

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 foci of t

NTA Abhyas JEE Main 2020 Solution View → 86

Let x 2 + y 2 = 4 r 2 and x y = 1 intersects at A and B in first quadrant. If A B = 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 x 2 a 2 - y 2 b 2 = 1 ( a < b ) , whose centre C be such that C P is perpendicular to C Q , then the value of 1 C P 2 + 1 C Q 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 2 x + y - 4 = 0 , then the equation of the hyperbola is

NTA Abhyas JEE Main 2020 Solution View → 90

From a point P , two tangents P A and P B 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 is

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 b a is

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 a sec ⁡ π 6 , b tan ⁡ π 6 form a triangle of area 3 a 2 sq. units with the coordinate axes. The eccentricity of the conj

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 = 8 x is

NTA Abhyas JEE Main 2020 Solution View → 94

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

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) is equal

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 = 2 x , y = - 2 x and the tangent at the point 5 , 4 on 4 x 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 equal to

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 l x + m y + 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 x y = c 2 is

NTA Abhyas JEE Main 2020 Solution View → 104

Values of m , for which the line y = m x + 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 + b is

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 15 x 2 + 3 y 2 = k

NTA Abhyas JEE Main 2020 Solution View → 107

If the eccentricity of the hyperbola x 2 - y 2 sec 2 ⁡ α = 5 is 3 times the eccentricity of the ellipse x 2 sec 2 ⁡ α + y 2 = 25 , then tan 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 = α x + 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 equa

NTA Abhyas JEE Main 2020 Solution View → 111

From a point P , two tangents P A and P B 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 wh

NTA Abhyas JEE Main 2020 Solution View → 112

A hyperbola has foci 4,2 , 2 , 2 and it passes through P 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 x 2 25 - y 2 36 = 1 which passes through the point 2 , 4 is a hyperbola, whose transverse axis length (in units) is equal t

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 3 x 2 + 4 y 2 = 12 , then its equation is

NTA Abhyas JEE Main 2020 Solution View → 115

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

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 &#8289; &#952; 2 - y 2 cos 2 &#8289; &#952; = 1 is 2 3 , then the sum of all the possible values of &#952; is (where, &#952; &#8712

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 = 10 &#955; , then the va

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 3 x - 4 y = 0 and 3 x + 4 y = 0 at Q and R respectivel

NTA Abhyas JEE Main 2020 Solution View → 120

Let the variable line y = k x + 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 coni

NTA Abhyas JEE Main 2020 Solution View →
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