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Parabola — JEE Main & Advanced Mathematics PYQs

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

411 questionsMathematicsSolutions on every page
1

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the tangent to the same parabola at another point (x₁, y₁) on the parabola. If L and T are perpendic

JEE Advanced 2026 Solution View → 2

Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the len

JEE Main 2026 Solution View → 3

Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of points P and Q are in the ratio 1:2 . If the chord PQ subtends an angle at the focus of the para

JEE Main 2026 Solution View → 4

Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing through the point P intersects the circle x^2 + y^2 - 2x - 4y + 3 = 0 at the points R and S , th

JEE Main 2026 Solution View → 5

Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B( , ) , > 1 , be a point on P such that the slope of AB is 3/5 . If BC is a focal chord of P , the

JEE Main 2026 Solution View → 6

Let A,B and C be the vertices of a variable right angled triangle inscribed in the parabola y^2=16x . Let the vertex B containing the right angle be (4,8) and the locus of the cent

JEE Main 2026 Solution View → 7

Consider the parabola P : y^2 = 4kx and the ellipse E : x^2 a^2 + y^2 b^2 = 1 . Let the line segment joining the points of intersection of P and E , be their latus rectums. If the

JEE Main 2026 Solution View → 8

Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the distance between its vertex and the x -axis is minimum. Then the value of p^2 + q^2 is:

JEE Main 2026 Solution View → 9

Let A be the focus of the parabola y²=8 x . Let the line y= m x+ c intersect the parabola at two distinct points B and C . If the centroid of the triangle A B C is ( 7 3 , 4 3 ) ,

JEE Main 2026 Solution View → 10

Let the image of parabola x²=4 y , in the line x-y=1 be (y+a)²=b(x-c) , a, b, c ~N . Then a+b+c is equal to

JEE Main 2026 Solution View → 11

An equilateral triangle OAB is inscribed in the parabola y²=4 x with the vertex O at the vertex of the parabola. Then the minimum distance of the circle having A B as a diameter fr

JEE Main 2026 Solution View → 12

Let the locus of the mid-point of the chord through the origin O of the parabola y²=4 x be the curve S. Let P be any point on S. Then the locus of the point, which internally divid

JEE Main 2026 Solution View → 13

If the chord joining the points P ₁ (x₁, y₁ ) and P ₂ (x₂, y₂ ) on the parabola y²=12 x subtends a right angle at the vertex of the parabola, then x₁ x₂-y₁ y₂ is equal to

JEE Main 2026 Solution View → 14

Let y²=12 x be the parabola with its vertex at O. Let P be a point on the parabola and A be a point on the x -axis such that OPA =90^ . Then the locus of the centroid of such trian

JEE Main 2026 Solution View → 15

Let one end of a focal chord of the parabola y²=16 x be (16,16) . If P ( , ) divides this focal chord internally in the ratio 5: 2 , then the minimum value of + is equal to :

JEE Main 2026 Solution View → 16

Let O be the vertex of the parabola x²=4 y and Q be any point on it. Let the locus of the point P, which divides the line segment OQ internally in the ratio 2: 3 be the conic C. Th

JEE Main 2026 Solution View → 17

Let S denote the locus of the mid-points of those chords of the parabola y^2=x , such that the area of the region enclosed between the parabola and the chord is 4 3 . Let R denote

JEE Advanced 2025 Solution View → 18

Let r be the radius of the circle, which touches x -axis at point ( a , 0), a 0 and the parabola y ^2=9 x at the point (4,6) . Then r is equal to ________

JEE Main 2025 Solution View → 19

Let P be the parabola, whose focus is (-2,1) and directrix is 2 x+y+2=0 . Then the sum of the ordinates of the points on P , whose abscissa is -2 , is

JEE Main 2025 Solution View → 20

The axis of a parabola is the line y=x and its vertex and focus are in the first quadrant at distances 2 and 2 2 units from the origin, respectively. If the point (1, k ) lies on t

JEE Main 2025 Solution View → 21

A line passing through the point A (-2,0) , touches the parabola P: y^2=x-2 at the point B in the first quadrant. The area, of the region bounded by the line AB , parabola P and th

JEE Main 2025 Solution View → 22

The radius of the smallest circle which touches the parabolas y=x^2+2 and x=y^2+2 is

JEE Main 2025 Solution View → 23

Let the point P of the focal chord P Q of the parabola y^2=16 x be (1,-4) . If the focus of the parabola divides the chord PQ in the ratio m : n , gcd (m, n)=1 , then m^2+n^2 is eq

JEE Main 2025 Solution View → 24

Let the focal chord P Q of the parabola y^2=4 x make an angle of 60^ with the positive x -axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being

JEE Main 2025 Solution View → 25

Let y^2=12 x be the parabola and S be its focus. Let PQ be a focal chord of the parabola such that ( SP )( SQ )= 147 4 . Let C be the circle described taking PQ as a diameter. If t

JEE Main 2025 Solution View → 26

Two parabolas have the same focus ((4,3) ) and their directrices are the (x )-axis and the (y )-axis, respectively. If these parabolas intersects at the points (A ) and (B ), then

JEE Main 2025 Solution View → 27

Let A and B be the two points of intersection of the line y+5=0 and the mirror image of the parabola y^2=4 x with respect to the line x+y+4=0 . If d denotes the distance between A

JEE Main 2025 Solution View → 28

Let A B C D be a trapezium whose vertices lie on the parabola y^2=4 x . Let the sides A D and B C of the trapezium be parallel to y -axis. If the diagonal AC is of length 25 4 and

JEE Main 2025 Solution View → 29

If the equation of the parabola with vertex V ( 3 2 , 3 ) and the directrix x+2 y=0 is x^2+ y^2- x y-30 x-60 y+225=0 , then + + is equal to :

JEE Main 2025 Solution View → 30

Let the shortest distance from ( a , 0), a 0 , to the parabola y^2=4 x be 4 . Then the equation of the circle passing through the point (a, 0) and the focus of the parabola, and ha

JEE Main 2025 Solution View → 31

The focus of the parabola y^2=4 x+16 is the centre of the circle C of radius 5 . If the values of , for which C passes through the point of intersection of the lines 3 x-y=0 and x+

JEE Main 2025 Solution View → 32

If the line 3 x-2 y+12=0 intersects the parabola 4 y=3 x^2 at the points A and B , then at the vertex of the parabola, the line segment A B subtends an angle equal to

JEE Main 2025 Solution View → 33

Let P (4,4 3 ) be a point on the parabola y^2=4 a x and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the direct

JEE Main 2025 Solution View → 34

Let the parabola y=x^2+ p x-3 , meet the coordinate axes at the points P , Q and R . If the circle C with centre at (-1,-1) passes through the points P, Q and R , then the area of

JEE Main 2025 Solution View → 35

Let A₁, B₁, C₁ be three points in the x y -plane. Suppose that the lines A₁ C₁ and B₁ C₁ are tangents to the curve y^2=8 x at A₁ and B₁ , respectively. If O=(0,0) and C₁=(-4,0) , t

JEE Advanced 2024 Solution View → 36

A normal with slope 1 6 is drawn from the point (0,- ) to the parabola x^2=-4 a y , where a>0 . Let L be the line passing through (0,- ) and parallel to the directrix of the parabo

JEE Advanced 2024 Solution View → 37

Let A, B and C be three points on the parabola y^2=6 x and let the line segment A B meet the line L through C parallel to the x -axis at the point D . Let M and N respectively be t

JEE Main 2024 Solution View → 38

Consider the circle C: x^2+y^2=4 and the parabola P: y^2=8 x . If the set of all values of , for which three chords of the circle C on three distinct lines passing through the poin

JEE Main 2024 Solution View → 39

Let a conic C pass through the point (4,-2) and P(x, y), x 3 , be any point on C . Let the slope of the line touching the conic C only at a single point P be half the slope of the

JEE Main 2024 Solution View → 40

Let L₁, L₂ be the lines passing through the point P(0,1) and touching the parabola 9 x^2+12 x+18 y-14=0 . Let Q and R be the points on the lines L₁ and L₂ such that the P Q R is an

JEE Main 2024 Solution View → 41

Let a line perpendicular to the line 2 x-y=10 touch the parabola y^2=4(x-9) at the point P . The distance of the point P from the centre of the circle x^2+y^2-14 x-8 y+56=0 is ____

JEE Main 2024 Solution View → 42

Suppose A B is a focal chord of the parabola y^2=12 x of length l and slope m < 3 . If the distance of the chord AB from the origin is d , then l ~d ^2 is equal to _______

JEE Main 2024 Solution View → 43

Let PQ be a chord of the parabola y^2=12 x and the midpoint of PQ be at (4,1) . Then, which of the following point lies on the line passing through the points P and Q?

JEE Main 2024 Solution View → 44

Let the length of the focal chord PQ of the parabola y^2=12 x be 15 units. If the distance of PQ from the origin is p , then 10 p ^2 is equal to _______

JEE Main 2024 Solution View → 45

The maximum area of a triangle whose one vertex is at ( 0 , 0 ) and the other two vertices lie on the curve y = - 2 x 2 + 54 at points ( x , y ) and ( - x , y ) where y > 0 is :

JEE Main 2024 Solution View → 46

Let P ( α , β ) be a point on the parabola y 2 = 4 x . If P also lies on the chord of the parabola x 2 = 8 y whose mid point is 1 , 5 4 , then ( α - 28 ) ( β - 8 ) is equal to ____

JEE Main 2024 Solution View → 47

If the shortest distance of the parabola y 2 = 4 x from the centre of the circle x 2 + y 2 - 4 x - 16 y + 64 = 0 is d , then d 2 is equal to :

JEE Main 2024 Solution View → 48

Let P be a point on the parabola y 2 = 4 a x , where a &#62; 0 . The normal to the parabola at P meets the x -axis at a point Q . The area of the triangle P F Q , where F is the fo

JEE Advanced 2023 Solution View → 49

Let P Q be a focal chord of the parabola y 2 = 36 x of length 100 , making an acute angle with the positive x - axis. Let the ordinate of P be positive and M be the point on the li

JEE Main 2023 Solution View → 50

Let a common tangent to the curves y 2 = 4 x and x - 4 2 + y 2 = 16 touch the curves at the points P and Q . Then P Q 2 is equal to ________.

JEE Main 2023 Solution View → 51

The ordinates of the points P and Q on the parabola with focus ( 3 , 0 ) and directrix x = - 3 are in the ratio 3 : 1 . If R ( &#945; , &#946; ) is the point of intersection of the

JEE Main 2023 Solution View → 52

Let R be the focus of the parabola y 2 = 20 x and the line y = m x + c intersect the parabola at two points P and Q . Let the points G 10 , 10 be the centroid of the triangle P Q R

JEE Main 2023 Solution View → 53

If the x -intercept of a focal chord of the parabola y 2 = 8 x + 4 y + 4 is 3 , then the length of this chord is equal to _____ .

JEE Main 2023 Solution View → 54

Let S be the set of all a &#8712; N such that the area of the triangle formed by the tangent at the point P b , c , b , c &#8712; N , on the parabola y 2 = 2 a x and the lines x =

JEE Main 2023 Solution View → 55

The parabolas : a x 2 + 2 b x + c y = 0 and d 2 + 2 e x + f y = 0 intersect on the line y = 1 . If a , b , c , d , e , f are positive real numbers and a , b , c are in G . P . , th

JEE Main 2023 Solution View → 56

Let A be a point on the x -axis. Common tangents are drawn from A to the curves x 2 + y 2 = 8 and y 2 = 16 x . If one of these tangents touches the two curves at Q and R , then Q R

JEE Main 2023 Solution View → 57

If P ( h , k ) be point on the parabola x = 4 y 2 , which is nearest to the point Q ( 0 , 33 ) , then the distance of P from the directrix of the parabola y 2 = 4 ( x + y ) is equa

JEE Main 2023 Solution View → 58

A triangle is formed by the tangents at the point ( 2 , 2 ) on the curves y 2 = 2 x and x 2 + y 2 = 4 x , and the line x + y + 2 = 0 . If r is the radius of its circumcircle, then

JEE Main 2023 Solution View → 59

The equations of two sides of a variable triangle are x = 0 and y = 3 , and its third side is a tangent to the parabola y 2 = 6 x . The locus of its circumcentre is :

JEE Main 2023 Solution View → 60

The distance of the point 6 , - 2 2 from the common tangent y = m x + c , m &#62; 0 , of the curves x = 2 y 2 and x = 1 + y 2 is

JEE Main 2023 Solution View → 61

The equations of sides A B and A C of a triangle A B C are &#955; + 1 x + &#955; y = 4 and &#955; x + 1 - &#955; y + &#955; = 0 respectively. Its vertex A is on the y - axis and it

JEE Main 2023 Solution View → 62

Let a tangent to the curve y 2 = 24 x meet the curve x y = 2 at the points A and B . Then the mid-points of such line segments A B lie on a parabola with the

JEE Main 2023 Solution View → 63

Consider the parabola y 2 = 4 x . Let S be the focus of the parabola. A pair of tangents drawn to the parabola from the point P = - 2 , 1 meet the parabola at P 1 and P 2 . Let Q 1

JEE Advanced 2022 Solution View → 64

Two tangent lines l 1 and l 2 are drawn from the point 2 , 0 to the parabola 2 y 2 = - x . If the lines l 1 and l 2 are also tangent to the circle x - 5 2 + y 2 = r , then 17 r^2 i

JEE Main 2022 Solution View → 65

If the tangents drawn at the points P and Q on the parabola y 2 = 2 x - 3 intersect at the point R 0 , 1 , then the orthocentre of the triangle P Q R is

JEE Main 2022 Solution View → 66

If the length of the latus rectum of a parabola, whose focus is a , a and the tangent at its vertex is x + y = a , is 16 , then a is equal to

JEE Main 2022 Solution View → 67

Let P a , b be a point on the parabola y 2 = 8 x such that the tangent at P passes through the centre of the circle x 2 + y 2 - 10 x - 14 y + 65 = 0 . Let A be the product of all p

JEE Main 2022 Solution View → 68

The equation of a common tangent to the parabolas y = x 2 and y = - x - 2 2 is

JEE Main 2022 Solution View → 69

The tangents at the points A 1 , 3 and B 1 , - 1 on the parabola y 2 - 2 x - 2 y = 1 meet at the point P . Then the area (in unit 2 ) of the triangle P A B is:

JEE Main 2022 Solution View → 70

The sum of diameters of the circles that touch (i) the parabola 75 x 2 = 64 5 y - 3 at the point 8 5 , 6 5 and (ii) the y -axis, is equal to _____ .

JEE Main 2022 Solution View → 71

Let P : y 2 = 4 a x , a &#62; 0 be a parabola with focus S .Let the tangents to the parabola P make an angle of &#960; 4 with the line y = 3 x + 5 touch the parabola P at A and B .

JEE Main 2022 Solution View → 72

If vertex of parabola is 2 , - 1 and equation of its directrix is 4 x - 3 y = 21 , then the length of latus rectum is

JEE Main 2022 Solution View → 73

If the equation of the parabola, whose vertex is at 5 , 4 and the directrix is 3 x + y - 29 = 0 , is x 2 + a y 2 + b x y + c x + d y + k = 0 , then a + b + c + d + k is equal to

JEE Main 2022 Solution View → 74

A circle of radius 2 unit passes through the vertex and the focus of the parabola y 2 = 2 x and touches the parabola y = x - 1 4 2 + &#945; , where &#945; &#62; 0 . Then 4 &#945; -

JEE Main 2022 Solution View → 75

Let the normal at the point P on the parabola y 2 = 6 x pass through the point 5 , - 8 . If the tangent at P to the parabola intersects its directrix at the point Q , then the ordi

JEE Main 2022 Solution View → 76

Let the common tangents to the curves 4 x 2 + y 2 = 9 and y 2 = 4 x intersect at the point Q . Let an ellipse, centered at the origin O , has lengths of semi-minor and semi-major a

JEE Main 2022 Solution View → 77

If y = m 1 x + c 1 and y = m 2 x + c 2 , m 1 &#8800; m 2 are two common tangents of circle x 2 + y 2 = 2 and parabola y 2 = x , then the value of 8 m 1 m 2 is equal to

JEE Main 2022 Solution View → 78

Let x = 2 t , y = t 2 3 be a conic. Let S be the focus and B be the point on the axis of the conic such that S A &#8869; B A , where A is any point on the conic. If k is the ordina

JEE Main 2022 Solution View → 79

Let P 1 be a parabola with vertex 3 , 2 and focus 4 , 4 and P 2 be its mirror image with respect to the line x + 2 y = 6 . Then the directrix of P 2 is x + 2 y = _____.

JEE Main 2022 Solution View → 80

A particle is moving in the x y -plane along a curve C passing through the point 3 , 3 . The tangent to the curve C at the point P meets the x -axis at Q . If the y -axis bisects t

JEE Main 2022 Solution View → 81

Let x 2 + y 2 + A x + B y + C = 0 be a circle passing through 0 , 6 and touching the parabola y = x 2 at 2 , 4 . Then A + C is equal to _____

JEE Main 2022 Solution View → 82

If two tangents drawn from a point &#945; , &#946; lying on the ellipse 25 x 2 + 4 y 2 = 1 to the parabola y 2 = 4 x are such that the slope of one tangent is four times the other,

JEE Main 2022 Solution View → 83

Let E denote the parabola y 2 = 8 x . Let P = - 2 , 4 , and let Q and Q ' be two distinct points on E such that the lines P Q and P Q ' are tangents to E . Let F be the focus of E

JEE Advanced 2021 Solution View → 84

Consider the region R= (x, y) R R : x 0 . and .y² 4-x . Let F be the family of all circles that are contained in R and have centers on the x -axis. Let C be the circle that has lar

JEE Advanced 2021 Solution View → 85

Consider the region R= (x, y) R R : x 0 . and .y² 4-x . Let F be the family of all circles that are contained in R and have centers on the x -axis. Let C be the circle that has lar

JEE Advanced 2021 Solution View → 86

Consider the parabola with vertex 1 2 , 3 4 and the directrix y = 1 2 . Let P be the point where the parabola meets the line x = - 1 2 . If the normal to the parabola at P intersec

JEE Main 2021 Solution View → 87

A tangent line L is drawn at the point 2 , - 4 on the parabola y 2 = 8 x . If the line L is also tangent to the circle x 2 + y 2 = a , then a is equal to .

JEE Main 2021 Solution View → 88

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x -axis at a distance R and S ( &#62; R ) respectively from the origin, is :

JEE Main 2021 Solution View → 89

If two tangents drawn from a point P to the parabola y 2 = 16 ( x - 3 ) are at right angles, then the locus of point P is:

JEE Main 2021 Solution View → 90

A tangent and a normal are drawn at the point P ( 2 , - 4 ) on the parabola y 2 = 8 x , which meet the directrix of the parabola at the points A and B respectively. If Q ( a , b )

JEE Main 2021 Solution View → 91

If a line along a chord of the circle 4 x 2 + 4 y 2 + 120 x + 675 = 0 , passes through the point ( - 30 , 0 ) and is tangent to the parabola y 2 = 30 x , then the length of this ch

JEE Main 2021 Solution View → 92

Let a parabola P be such that its vertex and focus lie on the positive x -axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from O ( 0 , 0 ) to

JEE Main 2021 Solution View → 93

Let P be a variable point on the parabola y = 4 x 2 + 1 . Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x

JEE Main 2021 Solution View → 94

If the point on the curve y 2 = 6 x , nearest to the point 3 , 3 2 is ( &#945; , &#946; ) , then 2 ( &#945; + &#946; ) is equal to _________.

JEE Main 2021 Solution View → 95

Let the tangent to the parabola S : y 2 = 2 x at the point P 2 , 2 meet the x - axis at Q and normal at it meet the parabola S at the point R . Then the area (in sq. units) of the

JEE Main 2021 Solution View → 96

Let y = m x + c , m &#62; 0 be the focal chord of y 2 = - 64 x , which is tangent to ( x + 10 ) 2 + y 2 = 4 . Then, the value of 4 2 ( m + c ) is equal to______

JEE Main 2021 Solution View → 97

Let C be the locus of the mirror image of a point on the parabola y 2 = 4 x with respect to the line y = x . Then the equation of tangent to C at P 2 , 1 is :

JEE Main 2021 Solution View → 98

If the three normals drawn to the parabola, y 2 = 2 x pass through the point a , 0 , a &#8800; 0 , then a must be greater than :

JEE Main 2021 Solution View → 99

A line is a common tangent to the circle x - 3 2 + y 2 = 9 and the parabola y 2 = 4 x . If the two points of contact a , b and c , d are distinct and lie in the first quadrant, the

JEE Main 2021 Solution View → 100

A tangent is drawn to the parabola y 2 = 6 x which is perpendicular to the line 2 x + y = 1 . Which of the following points does NOT lie on it?

JEE Main 2021 Solution View → 101

If P is a point on the parabola y = x 2 + 4 which is closest to the straight line y = 4 x - 1 , then the co-ordinates of P are:

JEE Main 2021 Solution View → 102

The locus of the mid-point of the line segment joining the focus of the parabola y 2 = 4 a x to a moving point of the parabola, is another parabola whose directrix is:

JEE Main 2021 Solution View → 103

The centre of the circle passing through the point 0 , 1 and touching the parabola y = x 2 at the point 2 , 4 is :

JEE Main 2020 Solution View → 104

Let L 1 be a tangent to the parabola y 2 = 4 ( x + 1 ) and L 2 be a tangent to the parabola y 2 = 8 ( x + 2 ) such that L 1 and L 2 intersect at right angles. Then L 1 and L 2 meet

JEE Main 2020 Solution View → 105

If the common tangent to the parabolas, y 2 = 4 x a n d x 2 = 4 y also touches the circle, x 2 + y 2 = c 2 , then c is equal to :

JEE Main 2020 Solution View → 106

Let the latus rectum of the parabola y 2 = 4 x be the common chord to the circles C 1 and C 2 each of them having radius 2 5 . Then, the distance between the centres of the circles

JEE Main 2020 Solution View → 107

Let P be a point on the parabola, y 2 = 12 x and N be the foot of the perpendicular drawn from P , on the axis of the parabola. A line is now drawn through the mid-point M of P N ,

JEE Main 2020 Solution View → 108

The area (in sq. units) of an equilateral triangle inscribed in the parabola y 2 = 8 x , with one of its vertices on the vertex of this parabola is

JEE Main 2020 Solution View → 109

If one end of a focal chord A B of the parabola y 2 = 8 x is at A 1 2 , - 2 , then the equation of the tangent to it at B is:

JEE Main 2020 Solution View → 110

Let a line y = m x m &#62; 0 , intersect the parabola, y 2 = x , at a point P , other than the origin. Let the tangent to it a P , meet the x -axis at the point Q . If area &#916;

JEE Main 2020 Solution View → 111

The locus of a point which divides the line segment joining the point 0 , - 1 and a point on the parabola x 2 = 4 y internally in the ratio 1 : 2 is:

JEE Main 2020 Solution View → 112

For a &#62; 0 , let the curves C 1 : y 2 = a x and C 2 : x 2 = a y intersect at origin O and a point P . Let the line x = b 0 &#60; b &#60; a intersect the chord O P and the x -axi

JEE Main 2020 Solution View → 113

If y = m x + 4 is a tangent to both the parabolas, y 2 = 4 x and x 2 = 2 b y , then b is equal to

JEE Main 2020 Solution View → 114

P is a point on the parabola whose ordinate equals its abscissa. A normal is drawn to the parabola at P to meet it again at Q . If S is the focus of the parabola, then the product

NTA Abhyas JEE Main 2020 Solution View → 115

If the line y - 2 = 0 is the directrix of the parabola x 2 - k y + 32 = 0 , k ≠ 0 and the parabola intersects the circle x 2 + y 2 = 8 at two real distinct points, then the absolut

NTA Abhyas JEE Main 2020 Solution View → 116

The coordinates of the focus of the parabola described parametrically by x = 5 t 2 + 2 , &#160; y = 10 t + 4 are

NTA Abhyas JEE Main 2020 Solution View → 117

The length of the chord of the parabola x 2 = 4 y having equation x - 2 y + 4 2 = 0 is

NTA Abhyas JEE Main 2020 Solution View → 118

The equation of the common tangent to the curves y 2 = 4 x and x 2 + 32 y = 0 is x + b y + c = 0 . The value of | sin &#8211; 1 ( sin &#160; 1 ) + sin &#8211; 1 ( sin &#160; b ) +

NTA Abhyas JEE Main 2020 Solution View → 119

The locus of the middle points of the chords of the parabola y 2 = 4 a x , which passes through the origin is

NTA Abhyas JEE Main 2020 Solution View → 120

If two parabolas y 2 = 4 a x – k and x 2 = 4 a y – k have only one common point P , then the equation of normal to y 2 = 4 a x – k at P is

NTA Abhyas JEE Main 2020 Solution View →
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