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Ellipse — JEE Main & Advanced Mathematics PYQs

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

313 questionsMathematicsSolutions on every page
1

Consider the ellipse E given by x^2 18 + y^2 12 = 1 . Let H be the hyperbola whose eccentricity is the reciprocal of the eccentricity of E and whose foci are the same as that of E

JEE Advanced 2026 Solution View → 2

Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let P be the point in the first quadrant where the given ellipses intersect. If is the acute a

JEE Advanced 2026 Solution View → 3

Let x^2 f(a^2+7a+3) + y^2 f(3a+15) = 1 represent an ellipse with major axis along y -axis, where f is a strictly decreasing positive function on R . If the set of all possible valu

JEE Main 2026 Solution View → 4

The eccentricity of an ellipse E with centre at the origin O is 3 2 and its directrices are x = 4 6 3 . Let H: x^2 a^2 - y^2 b^2 = 1 be a hyperbola whose eccentricity is equal to t

JEE Main 2026 Solution View → 5

Let x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity is 1 3 . Let P( , 0) , > 0 , be a focus of E and AB be a chord passing through P . Then th

JEE Main 2026 Solution View → 6

Let a focus of the ellipse E: x^2 a^2 + y^2 b^2 = 1 be S(4, 0) and its eccentricity be 4 5 . If the point P(3, ) lies on E and O is the origin, then the area of POS is equal to:

JEE Main 2026 Solution View → 7

Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 + y^2 = 36 internally. Let the curve C be the locus of the point B. If the eccentricity of C is

JEE Main 2026 Solution View → 8

Let an ellipse x^2 a^2 + y^2 b^2 = 1 , a < b , pass through the point (4, 3) and have eccentricity 5 3 . Then the length of its latus rectum is :

JEE Main 2026 Solution View → 9

An ellipse has its center at (1,-2) , one focus at (3,-2) and one vertex at (5,-2) . Then the length of its latus rectum is :

JEE Main 2026 Solution View → 10

Let the ellipse E : x² 144 + y² 169 =1 and the hyperbola H : x² 16 - y² ² =-1 have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum

JEE Main 2026 Solution View → 11

Let the length of the latus rectum of an ellipse x² a² + y² b² =1,(a>b) , be 30. If its eccentricity is the maximum value of the function f(t)=- 3 4 +2 t-t² , then ( a²+b² ) is equ

JEE Main 2026 Solution View → 12

Let (h, k) lie on the circle C : x²+y²=4 and the point (2 h+1,3 k+2) lie on an ellipse with eccentricity e . Then the value of 5 e² is equal to _ _ _ _ .

JEE Main 2026 Solution View → 13

Let each of the two ellipses E ₁: x² a² + y² b² =1,(a>b) and E ₂: x² ~A ² + y² ~B ² =1,( ~A < B ) have eccentricity 4 5 . Let the lengths of the latus recta of E₁ and E₂ be l₁ and

JEE Main 2026 Solution View → 14

Let the line y-x=1 intersect the ellipse x² 2 + y² 1 =1 at the points A and B. Then the angle made by the line segment AB at the center of the ellipse is :

JEE Main 2026 Solution View → 15

Let S and S ^ be the foci of the ellipse x² 25 + y² 9 =1 and P ( , ) be a point on the ellipse in the first quadrant. If ( SP )²+ ( S ^ P )²- SP S ^ P =37 , then ²+ ² is equal to :

JEE Main 2026 Solution View → 16

If the line x+4 y= 7 , where R , touches the ellipse 3 x²+4 y²=1 at the point P in the first quadrant, then one of the focal distances of P is :

JEE Main 2026 Solution View → 17

Let P (x₁, y₁ ) and Q (x₂, y₂ ) be two distinct points on the ellipse x^2 9 + y^2 4 =1 such that y₁>0 , and y₂>0 . Let C denote the circle x^2+y^2=9 , and M be the point (3,0) . Su

JEE Advanced 2025 Solution View → 18

Let the ellipse 3 x^2+ py ^2=4 pass through the centre C of the circle x^2+y^2-2 x-4 y-11=0 of radius r . Let f₁, f₂ be the focal distances of the point C on the ellipse. Then 6 f₁

JEE Main 2025 Solution View → 19

Let A= ( , ) R R :| -1| 4 and | -5| 6 and B= ( , ) R R : 16( -2)^2+9( -6)^2 144

JEE Main 2025 Solution View → 20

Let the length of a latus rectum of an ellipse x^2 a^2 + y^2 b^2 =1 be 10 . If its eccentricity is the minimum value of the function f( t )= t ^2+ t + 11 12 , t R , then a ^2+ b ^2

JEE Main 2025 Solution View → 21

The centre of a circle C is at the centre of the ellipse E: x^2 a^2 + y^2 b^2 =1, a b . Let C pass through the foci F₁ and F₂ of E such that the circle C and the ellipse E intersec

JEE Main 2025 Solution View → 22

Let for two distinct values of p the lines y=x+p touch the ellipse E : x ^2 4^2 + y ^2 3^2 =1 at the points A and B . Let the line y = x intersect E at the points C and D . Then th

JEE Main 2025 Solution View → 23

The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2,-3) and eccentricity is 4 5 , is

JEE Main 2025 Solution View → 24

Let C be the circle x ^2+( y -1)^2=2, E ₁ and E ₂ be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line x+y=

JEE Main 2025 Solution View → 25

Let C be the circle of minimum area enclosing the ellipse E: x^2 a^2 + y^2 b^2 =1 with eccentricity 1 2 and foci ( 2,0) . Let PQR be a variable triangle, whose vertex P is on the c

JEE Main 2025 Solution View → 26

A line passing through the point P ( 5 , 5 ) intersects the ellipse x ^2 36 + y ^2 25 =1 at A and B such that (P A) .(P B) is maximum. Then 5 (P A^2+P B^2 ) is equal to :

JEE Main 2025 Solution View → 27

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :

JEE Main 2025 Solution View → 28

If S and S^ are the foci of the ellipse x^2 18 + y^2 9 =1 and P be a point on the ellipse, then (S P . S^ P )+ ( SP . S ^ P ) is equal to :

JEE Main 2025 Solution View → 29

If x+ y=109 is the equation of the chord of the ellipse x^2 9 + y^2 4 =1 , whose mid point is ( 5 2 , 1 2 ) , then + is equal to :

JEE Main 2025 Solution View → 30

Let the ellipse ( E ₁: x^2 a ^2 + y^2 ~b ^2 =1, a b ) and ( E ₂: x^2 ~A ^2 + y^2 ~B ^2 =1, ~A B ) have same eccentricity ( 1 3 ). Let the product of their lengths of latus rectums

JEE Main 2025 Solution View → 31

If the midpoint of a chord of the ellipse x^2 9 + y^2 4 =1 is ( 2 , 4 / 3) , and the length of the chord is 2 3 , then is :

JEE Main 2025 Solution View → 32

Let E ₁: x^2 9 + y^2 4 =1 be an ellipse. Ellipses E ₁ 's are constructed such that their centres and eccentricities are same as that of E₁ , and the length of minor axis of E_i is

JEE Main 2025 Solution View → 33

The equation of the chord, of the ellipse x^2 25 + y^2 16 =1 , whose mid-point is (3,1) is :

JEE Main 2025 Solution View → 34

Let the product of the focal distances of the point ( 3 , 1 2 ) on the ellipse x^2 a^2 + y^2 b^2 =1,( a b ) , be 7 4 . Then the absolute difference of the eccentricities of two suc

JEE Main 2025 Solution View → 35

The length of the chord of the ellipse x^2 4 + y^2 2 =1 , whose mid-point is (1, 1 2 ) , is :

JEE Main 2025 Solution View → 36

Consider the ellipse x^2 9 + y^2 4 =1 . Let S(p, q) be a point in the first quadrant such that p^2 9 + q^2 4 >1 . Two tangents are drawn from S to the ellipse, of which one meets t

JEE Advanced 2024 Solution View → 37

Let f(x)=x^2+9, g(x)= x x-9 and a =f g(10), b =g f(3) . If e and l denote the eccentricity and the length of the latus rectum of the ellipse x^2 a + y^2 b =1 , then 8 e ^2+l^2 is e

JEE Main 2024 Solution View → 38

Let the line 2 x+3 y- k =0, k >0 , intersect the x -axis and y -axis at the points A and B , respectively. If the equation of the circle having the line segment AB as a diameter is

JEE Main 2024 Solution View → 39

Let P be a point on the ellipse x 2 9 + y 2 4 = 1 . Let the line passing through P and parallel to y - axis meet the circle x 2 + y 2 = 9 at point Q such that P and Q are on the sa

JEE Main 2024 Solution View → 40

Let P be a parabola with vertex 2 , 3 and directrix 2 x + y = 6 . Let an ellipse E : x 2 a 2 + y 2 b 2 = 1 , a > b of eccentricity 1 2 pass through the focus of the parabola P . Th

JEE Main 2024 Solution View → 41

Let A ( α , 0 ) and B ( 0 , β ) be the points on the line 5 x + 7 y = 50 . Let the point P divide the line segment A B internally in the ratio 7 : 3 . Let 3 x - 25 = 0 be a directr

JEE Main 2024 Solution View → 42

If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :

JEE Main 2024 Solution View → 43

If the points of intersection of two distinct conics x 2 + y 2 = 4 b and x 2 16 + y 2 b 2 = 1 lie on the curve y 2 = 3 x 2 , then 3 3 times the area of the rectangle formed by the

JEE Main 2024 Solution View → 44

The length of the chord of the ellipse x 2 25 + y 2 16 = 1 , whose mid point is 1 , 2 5 , is equal to:

JEE Main 2024 Solution View → 45

Let T 1 and T 2 be two distinct common tangents to the ellipse E : x 2 6 + y 2 3 = 1 and the parabola P : y 2 = 12 x . Suppose that the tangent T 1 touches P and E at the points A

JEE Advanced 2023 Solution View → 46

Let an ellipse with centre 1 , 0 and latus rectum of length 1 2 have its major axis along x-axis. If its minor axis subtends an angle 60 &#8728; at the foci, then the square of the

JEE Main 2023 Solution View → 47

Let the tangent and normal at the point 3 3 , 1 on the ellipse x 2 36 + y 2 4 = 1 meet the y - axis at the points A and B respectively. Let the circle C be drawn taking A B as a di

JEE Main 2023 Solution View → 48

Let P 2 3 7 , 6 7 , Q , R and S be four points on the ellipse 9 x 2 + 4 y 2 = 36 . Let P Q and R S be mutually perpendicular and pass through the origin. If 1 P Q 2 + 1 R S 2 = p q

JEE Main 2023 Solution View → 49

If the radius of the largest circle with centre ( 2 , 0 ) inscribed in the ellipse x 2 + 4 y 2 = 36 is r , then 12 r 2 is equal to

JEE Main 2023 Solution View → 50

Let a circle of radius 4 be concentric to the ellipse 15 x 2 + 19 y 2 = 285 . Then the common tangents are inclined to the minor axis of the ellipse at the angle

JEE Main 2023 Solution View → 51

Let the ellipse E : x 2 + 9 y 2 = 9 intersect the positive x - and y -axes at the points A and B respectively. Let the major axis of E be a diameter of the circle C . Let the line

JEE Main 2023 Solution View → 52

The line x = 8 is the directrix of the ellipse E : x 2 a 2 + y 2 b 2 = 1 with the corresponding focus 2 , 0 . If the tangent to E at the point P in the first quadrant passes throug

JEE Main 2023 Solution View → 53

If the tangent at a point P on the parabola y 2 = 3 x is parallel to the line x + 2 y = 1 and the tangents at the points Q and R on the ellipse x 2 4 + y 2 1 = 1 are perpendicular

JEE Main 2023 Solution View → 54

Let a tangent to the curve 9 x 2 + 16 y 2 = 144 intersect the coordinate axes at the points A and B . Then, the minimum length of the line segment A B is ______

JEE Main 2023 Solution View → 55

Let C be the largest circle centred at 2 , 0 and inscribed in the ellipse x 2 36 + y 2 16 = 1 . If 1 , &#945; lies on C , then 10 &#945; 2 is equal to ______

JEE Main 2023 Solution View → 56

Consider the ellipse x 2 4 + y 2 3 = 1 . Let H &#945; , 0 , 0 &#60; &#945; &#60; 2 , be a point. A straight line drawn through H parallel to the y -axis crosses the ellipse and its

JEE Advanced 2022 Solution View → 57

Let S = x , y &#8712; &#8469; &#215; &#8469; : 9 x - 3 2 + 16 y - 4 2 &#8804; 144 and T = x , y &#8712; &#8477; &#215; &#8477; : x - 7 2 + y - 4 2 &#8804; 36 The n S &#8745; T is e

JEE Main 2022 Solution View → 58

Let the tangents at the points P and Q on the ellipse x 2 2 + y 2 4 = 1 meet at the point R 2 , 2 2 - 2 . If S is the focus of the ellipse on its negative major axis, then S P 2 +

JEE Main 2022 Solution View → 59

If the length of the latus rectum of the ellipse x 2 + 4 y 2 + 2 x + 8 y - &#955; = 0 is 4 , and l is the length of its major axis, then &#955; + l is equal to _____.

JEE Main 2022 Solution View → 60

The acute angle between the pair of tangents drawn to the ellipse 2 x 2 + 3 y 2 = 5 from the point 1 , 3 is

JEE Main 2022 Solution View → 61

If the ellipse x 2 a 2 + y 2 b 2 = 1 meets the line x 7 + y 2 6 = 1 on the x -axis and the line x 7 - y 2 6 = 1 on the y -axis, then the eccentricity of the ellipse is

JEE Main 2022 Solution View → 62

Let P Q be a focal chord of the parabola y 2 = 4 x such that it subtends an angle of &#960; 2 at the point 3 , 0 . Let the line segment P Q be also a focal chord of the ellipse E :

JEE Main 2022 Solution View → 63

Let the eccentricity of an ellipse x 2 a 2 + y 2 b 2 = 1 , a &#62; b , be 1 4 . If this ellipse passes through the point - 4 2 5 , 3 , then a 2 + b 2 is equal to

JEE Main 2022 Solution View → 64

If m is the slope of a common tangent to the curves x 2 16 + y 2 9 = 1 and x 2 + y 2 = 12 , then 12 m 2 is equal to

JEE Main 2022 Solution View → 65

The locus of the mid-point of the line segment joining the point 4 , 3 and the points on the ellipse x 2 + 2 y 2 = 4 is an ellipse with eccentricity

JEE Main 2022 Solution View → 66

The line y = x + 1 meets the ellipse x 2 4 + y 2 2 = 1 at two points P and Q . If r is the radius of the circle with P Q as diameter then 3 r 2 is equal to

JEE Main 2022 Solution View → 67

Let the maximum area of the triangle that can be inscribed in the ellipse x 2 a 2 + y 2 4 = 1 , a &#62; 2 , having one of its vertices at one end of the major axis of the ellipse a

JEE Main 2022 Solution View → 68

Let E be the ellipse x 2 16 + y 2 9 = 1 . For any three distinct points P , Q and Q &#39; on E , let M P , Q be the mid-point of the line segment joining P and Q , and M P , Q &#39

JEE Advanced 2021 Solution View → 69

Let &#952; be the acute angle between the tangents to the ellipse x 2 9 + y 2 1 = 1 and the circle x 2 + y 2 = 3 at their point of intersection in the first quadrant. Then tan &#95

JEE Main 2021 Solution View → 70

The locus of mid-points of the line segments joining - 3 , - 5 and the points on the ellipse x 2 4 + y 2 9 = 1 is :

JEE Main 2021 Solution View → 71

The line 12 x cos &#952; + 5 y sin &#952; = 60 is tangent to which of the following curves ?

JEE Main 2021 Solution View → 72

If the minimum area of the triangle formed by a tangent to the ellipse x 2 b 2 + y 2 4 a 2 = 1 and the co-ordinate axis is k a b , then k is equal to ___________.

JEE Main 2021 Solution View → 73

On the ellipse x 2 8 + y 2 4 = 1 , let P be a point in the second quadrant such that the tangent at P to the ellipse is perpendicular to the line x + 2 y = 0 . Let S and S &#39; be

JEE Main 2021 Solution View → 74

Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its centre at 3 , - 4 , one focus at 4 , - 4 and one vertex at 5 , - 4 . If m x - y = 4 , m &#62; 0 is

JEE Main 2021 Solution View → 75

A ray of light through 2 , 1 is reflected at a point P on the y - axis and then passes through the point 5 , 3 . If this reflected ray is the directrix of an ellipse with eccentric

JEE Main 2021 Solution View → 76

If a tangent to the ellipse x 2 + 4 y 2 = 4 meets the tangents at the extremities of its major axis at B and C , then the circle with B C as diameter passes through the point.

JEE Main 2021 Solution View → 77

Let an ellipse E : x 2 a 2 + y 2 b 2 = 1 , a 2 &#62; b 2 , passes through 3 2 , 1 and has eccentricity 1 3 . If a circle, centered at focus F ( &#945; , 0 ) , &#945; &#62; 0 , of E

JEE Main 2021 Solution View → 78

Let E 1 : x 2 a 2 + y 2 b 2 = 1 , a &#62; b . Let E 2 be another ellipse such that it touches the end points of major axis of E 1 and the foci of E 2 are the end points of minor ax

JEE Main 2021 Solution View → 79

Let a tangent be drawn to the ellipse x 2 27 + y 2 = 1 at ( 3 3 cos &#952; , sin &#952; ) where &#952; &#8712; 0 , &#960; 2 . Then the value of &#952; such that the sum of intercep

JEE Main 2021 Solution View → 80

Let L be a tangent line to the parabola y 2 = 4 x - 20 at 6 , 2 . If L is also a tangent to the ellipse x 2 2 + y 2 b = 1 , then the value of b is equal to :

JEE Main 2021 Solution View → 81

If the points of intersection of the ellipse x 2 16 + y 2 b 2 = 1 and the circle x 2 + y 2 = 4 b , b &#62; 4 lie on the curve y 2 = 3 x 2 , then b is equal to :

JEE Main 2021 Solution View → 82

Let L be a common tangent line to the curves 4 x 2 + 9 y 2 = 36 and 2 x 2 + 2 y 2 = 31 . Then the square of the slope of the line L is ______.

JEE Main 2021 Solution View → 83

If the curve x 2 + 2 y 2 = 2 intersects the line x + y = 1 at two points P and Q , then the angle subtended by the line segment P Q at the origin is

JEE Main 2021 Solution View → 84

If the curves, x 2 a + y 2 b = 1 and x 2 c + y 2 d = 1 intersect each other at an angle of 90 &#176; , then which of the following relations is TRUE?

JEE Main 2021 Solution View → 85

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies :

JEE Main 2020 Solution View → 86

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x 2 4 + y 2 2 = 1 from any of its foci?

JEE Main 2020 Solution View → 87

If the co-ordinates of two points A and B are ( 7 , 0 ) and ( - 7 , 0 ) respectively and P is any point on the conic, 9 x 2 + 16 y 2 = 144 , then P A + P B is equal to :

JEE Main 2020 Solution View → 88

If the point P on the curve, 4 x 2 + 5 y 2 = 20 is farthest from the point Q 0 , - 4 , then P Q 2 is equal to

JEE Main 2020 Solution View → 89

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is 1 2 . If P ( 1 , &#946; ) , &#946; &#62; 0 is a point on this ellipse, then the equatio

JEE Main 2020 Solution View → 90

Let x 2 a 2 + y 2 b 2 = 1 a &#62; b be a given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, &#981; t = 5 12 + t - t 2 , t

JEE Main 2020 Solution View → 91

The length of the minor axis (along y -axis) of an ellipse in the standard form is 4 3 . If this ellipse touches the line x + 6 y = 8 then its eccentricity is:

JEE Main 2020 Solution View → 92

Let the line y = m x and the ellipse 2 x 2 + y 2 = 1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at - 1 3 2 , 0 and

JEE Main 2020 Solution View → 93

If 3 x + 4 y = 12 2 is a tangent o the ellipse x 2 a 2 + y 2 9 = 1 for some a &#8712; R , then the distance between the foci of the ellipse is

JEE Main 2020 Solution View → 94

If the distance between the foci of an ellipse is 6 and the distance between its directrix is 12 , then the length of its latus rectum is

JEE Main 2020 Solution View → 95

The angle between the pair of tangents drawn to the ellipse 3 x 2 + 2 y 2 = 5 from the point 1 , 2 is tan − 1 12 λ , then the value of λ is

NTA Abhyas JEE Main 2020 Solution View → 96

If the line x - 2 y = 12 is a tangent to the ellipse x 2 a 2 + y 2 b 2 = 1 at the point 3 , - 9 2 , then the length of the latus rectum of the ellipse is

NTA Abhyas JEE Main 2020 Solution View → 97

The point, which is at the shortest distance from the line x + y = 7 and lying on an ellipse x 2 + 2 y 2 = 6 , has coordinates ( a , b ) then the value of a b is

NTA Abhyas JEE Main 2020 Solution View → 98

If the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse x 2 40 + y 2 10 = 1 is x 2 + y 2 2 = a x 2 + b y 2 , then a – b is equal to

NTA Abhyas JEE Main 2020 Solution View → 99

If common tangents of x 2 + y 2 = r 2 and x 2 16 + y 2 9 = 1 forms a square, then the length of diagonal of the square is

NTA Abhyas JEE Main 2020 Solution View → 100

If a tangent of slope 2 of the ellipse x 2 a 2 + y 2 1 = 1 passes through the point - 2,0 , then the value of a 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 101

Let from a point A h , k chord of contacts are drawn to the ellipse x 2 + 2 y 2 = 6 such that all these chords touch the ellipse x 2 + 4 y 2 = 4 , then locus of the point A is

NTA Abhyas JEE Main 2020 Solution View → 102

If any tangent to the ellipse 25 x 2 + 9 y 2 = 225 meets the coordinate axes at A and B such that O A = O B then, the length A B is equal to (where, O is the origin)

NTA Abhyas JEE Main 2020 Solution View → 103

If the normal to the ellipse x 2 25 + y 2 1 = 1 is at a distance p from the origin, then the maximum value of p is

NTA Abhyas JEE Main 2020 Solution View → 104

Suppose S and S ′ are foci of the ellipse x 2 25 + y 2 16 = 1 . If P is a variable point on the ellipse and if ∆ is the area (in sq. units) of the triangle P S S ′ , then the maxim

NTA Abhyas JEE Main 2020 Solution View → 105

The line 2 x + y = 3 cuts the ellipse 4 x 2 + y 2 = 5 at points P and Q . If θ is the acute angle between the normals at P and Q , then θ is equal to

NTA Abhyas JEE Main 2020 Solution View → 106

A tangent having slope - 4 3 to the ellipse x 2 18 + y 2 32 = 1 intersects the major and minor axes at A and B . If O is the origin, then the area of Δ O A B is

NTA Abhyas JEE Main 2020 Solution View → 107

An ellipse has foci 4,2 , &#160; 2,2 and it passes through the point P 2,4 . The eccentricity of the ellipse is

NTA Abhyas JEE Main 2020 Solution View → 108

The line 2 x + y = 3 interesects the ellipse 4 x 2 + y 2 = 5 at two points. The point of intersection of the tangents to the ellipse at these points is

NTA Abhyas JEE Main 2020 Solution View → 109

Let the line y = m x and the ellipse 2 x 2 + y 2 = 1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at - 1 3 2 , 0 and

NTA Abhyas JEE Main 2020 Solution View → 110

The length of the latus rectum of the curve represented by x = 3 cos ⁡ t + sin ⁡ t and y = 4 cos ⁡ t - sin ⁡ t , is

NTA Abhyas JEE Main 2020 Solution View → 111

If m 1 and m 2 are the slopes of the tangents to the ellipse x 2 16 + y 2 9 = 1 which passes through 5,4 , then the value of m 1 + m 2 - m 1 m 2 is equal to

NTA Abhyas JEE Main 2020 Solution View → 112

If P and Q are points with eccentric angles θ and θ + π 6 on the ellipse x 2 16 + y 2 4 = 1 , then the area (in sq. units) of the triangle O P Q (where O is the origin) is equal to

NTA Abhyas JEE Main 2020 Solution View → 113

If y = x + c touches the ellipse 3 x 2 + 4 y 2 = 12 at the point P , then the value of the length O P (where O is the origin) is equal to

NTA Abhyas JEE Main 2020 Solution View → 114

If θ is the angle between the pair of tangents drawn to the ellipse 3 x 2 + 2 y 2 = 5 from the point 1,2 , then the value of tan 2 θ is equal to

NTA Abhyas JEE Main 2020 Solution View → 115

The focus and corresponding directrix of an ellipse are 3,4 and x + y - 1 = 0 respectively. If the eccentricity of the ellipse is 1 2 , then the coordinates of the centre of the el

NTA Abhyas JEE Main 2020 Solution View → 116

If 0,3 + 5 is a point on the ellipse whose foci are 2,3 and - 2,3 , then the length of the semi-major axis is

NTA Abhyas JEE Main 2020 Solution View → 117

Let S and S ′ are the focii of the ellipse x = 3 + 5 cos ⁡ θ , y = - 2 + 4 sin ⁡ θ . If B is one of the ends of one of the latus rectum, then the area (in sq. units) of the triangl

NTA Abhyas JEE Main 2020 Solution View → 118

The length of the portion of the common tangent to x 2 + y 2 = 16 and 9 x 2 + 25 y 2 = 225 between the two points of contact is

NTA Abhyas JEE Main 2020 Solution View → 119

Let there are exactly two points on the ellipse x 2 a 2 + y 2 b 2 = 1 whose distances from 0,0 are equal to a 2 2 + b 2 . Then, the eccentricity of the ellipse is equal to

NTA Abhyas JEE Main 2020 Solution View → 120

The point on the ellipse x 2 6 + y 2 3 = 1 which is nearest to the line x + y = 7 is

NTA Abhyas JEE Main 2020 Solution View →
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