MEDIUM

JEE Main

IMPORTANT

Earn 100

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 ordinate of the point $Q$ is

50% studentsanswered this correctly

Important Questions on Parabola

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 26 June 2022 Shift 1>Q 58

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 axes equal to

O Q

and

6

, respectively. If

e

and

l

respectively denote the eccentricity and the length of the latus rectum of this ellipse, then

\frac{l}{e^{2}}

is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 27 June 2022 Shift 1>Q 59

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 - \frac{1}{4})}^{2} + α

, where

α > 0

. Then

{(4 α - 8)}^{2}

is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 27 June 2022 Shift 2>Q 60

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

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 28 June 2022 Shift 2>Q 61

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

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 29 June 2022 Shift 2>Q 62

Let

P : y^{2} = 4 a x, a > 0

be a parabola with focus

S

.Let the tangents to the parabola

P

make an angle of

\frac{π}{4}

with the line

y = 3 x + 5

touch the parabola

P

A

and

B

. Then the value of

a

for which

A, B

and

S

are collinear is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 25 July 2022 Shift 1>Q 63

The sum of diameters of the circles that touch the parabola

75 x^{2} = 64 (5 y - 3)

at the point

(\frac{8}{5}, \frac{6}{5})

and the

y

-axis, is equal to _____ .

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 25 July 2022 Shift 2>Q 64

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:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 26 July 2022 Shift 1>Q 65

Let the function

f (x) = 2 x^{2} - \log_{e} x, x > 0

, be decreasing in

(0, a)

and increasing in

(a, 4)

. A tangent to the parabola

y^{2} = 4 a x

at a point

P

on it passes through the point

(8 a, 8 a - 1)

but does not pass through the point

(- \frac{1}{a}, 0)

. If the equation of the normal at

P

\frac{x}{α} + \frac{y}{β} = 1

, then

α + β

is equal to

Let the normal at the point P on the parabola y2=6x pass through the point 5,-8. If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is

Important Questions on Parabola

Learn and Prepare for any exam you want !

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 ordinate of the point $Q$ is