MEDIUM

JEE Main

IMPORTANT

Earn 100

Let the tangent drawn to the parabola $y^{2} = 24 x$ at the point $(α, β)$ is perpendicular to the line $2 x + 2 y = 5$ . Then the normal to the hyperbola $\frac{x^{2}}{α^{2}} - \frac{y^{2}}{β^{2}} = 1$ at the point $(α + 4, β + 4)$ does NOT pass through the point:

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Important Questions on Hyperbola

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 26 July 2022 Shift 2>Q 44

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

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 27 July 2022 Shift 1>Q 45

An ellipse

E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

passes through the vertices of the hyperbola

H : \frac{x^{2}}{49} - \frac{y^{2}}{64} = - 1

. Let the major and minor axes of the ellipse

E

coincide with the transverse and conjugate axes of the hyperbola

H

. Let the product of the eccentricities of

E

and

H

\frac{1}{2}

. If

l

is the length of the latus rectum of the ellipse

E

, then the value of

113 l

is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 28 July 2022 Shift 1>Q 46

For the hyperbola $H : x^{2} - y^{2} = 1$ and the ellipse $E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, a > b > 0$ , let the

(1) eccentricity of $E$ be reciprocal of the eccentricity of $H$ , and

(2) the line $y = \sqrt{\frac{5}{2}} x + K$ be a common tangent of $E$ and $H$ .

Then $4 (a^{2} + b^{2})$ is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 28 July 2022 Shift 2>Q 47

Let the hyperbola

H : \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

pass through the point

(2 \sqrt{2}, - 2 \sqrt{2})

. A parabola is drawn whose focus is same as the focus of

H

with positive abscissa and the directrix of the parabola passes through the other focus of

H

. If the length of the latus rectum of the parabola is e times the length of the latus rectum of

H

, where

e

is the eccentricity of

H

, then which of the following points lies on the parabola?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 29 July 2022 Shift 1>Q 48

Let the focal chord of the parabola

P : y^{2} = 4 x

along the line

L : y = m x + c, m > 0

meet the parabola at the points

M

and

N

. Let the line

L

be a tangent to the hyperbola

H : x^{2} - y^{2} = 4

. If

O

is the vertex of

P

and

F

is the focus of

H

on the positive

x

-axis, then the area of the quadrilateral

O M F N

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 25 January 2023 Shift 1>Q 49

The vertices of a hyperbola

H

are

(\pm 6, 0)

and its eccentricity is

\frac{\sqrt{5}}{2}

. Let

N

be the normal to

H

at a point in the first quadrant and parallel to the line

\sqrt{2} x + y = 2 \sqrt{2}

. If

d

is the length of the line segment of

N

between

H

and the

y

-axis then

d^{2}

is equal to _____ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 31 January 2023 Shift 2>Q 50

Let

H

be the hyperbola, whose foci are

(1 \pm \sqrt{2}, 0)

and eccentricity is

\sqrt{2}

. Then the length of its latus rectum is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 1 February 2023 Shift 2>Q 51

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

\sqrt{2} (y_{0} - x_{0})

is equal to :

Let the tangent drawn to the parabola y2=24x at the point α,β is perpendicular to the line 2x+2y=5. Then the normal to the hyperbola x2α2-y2β2=1 at the point α+4,β+4 does NOT pass through the point:

Important Questions on Hyperbola

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Let the tangent drawn to the parabola $y^{2} = 24 x$ at the point $(α, β)$ is perpendicular to the line $2 x + 2 y = 5$ . Then the normal to the hyperbola $\frac{x^{2}}{α^{2}} - \frac{y^{2}}{β^{2}} = 1$ at the point $(α + 4, β + 4)$ does NOT pass through the point: