EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 10th January 2019 Shift 1>Q 22

EASY

JEE Main

IMPORTANT

Earn 100

The equation of a tangent to the hyperbola, $4 x^{2} - 5 y^{2} = 20,$ parallel to the line $x - y = 2,$ is

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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 - 10th January 2019 Shift 2>Q 23

Let

S = \{(x, y) \in R^{2} : \frac{y^{2}}{1 + r} - \frac{x^{2}}{1 - r} = 1\},

where

r \neq \pm 1 .

Then

S

represents:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 12th April 2019 Shift 1>Q 24

Let

P

be the point of intersection of the common tangents to the parabola

y^{2} = 12 x

and the hyperbola

8 x^{2} - y^{2} = 8

. If

S

and

S^{'}

denote the foci of the hyperbola where

S

lies on the positive

x

-axis then

P

divides

S S^{'}

in a ratio:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 12th January 2019 Shift 1>Q 25

If the vertices of a hyperbola be at

(- 2, 0)

and

(2, 0)

and one of its foci be at

(- 3, 0)

, then which one of the following points does not lie on this hyperbola ?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 8th April 2018>Q 26

Tangents are drawn to the hyperbola

4 x^{2} - y^{2} = 36

at the points

P

and

Q

. If these tangents intersect at the point

T (0, 3)

then the area (in sq. units) of

Δ P T Q

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 15th April 2018>Q 27

If the tangent drawn to the hyperbola

4 y^{2} = x^{2} + 1

intersect the co-ordinates axes at the distinct points

A

and

B

, then the locus of the midpoint of

A B

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 2nd April 2017>Q 28

A hyperbola passes through the point

P (\sqrt{2}, \sqrt{3})

and has foci at

(\pm 2, 0)

. Then the tangent to this hyperbola at

P

also passes through the point

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 8th April 2017>Q 29

The locus of the point of intersection of the straight lines,

t x - 2 y - 3 t = 0

and

x - 2 t y + 3 = 0 (t \in R),

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 9th April 2016>Q 30

Let

a

and

b

respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation

9 e^{2} - 18 e + 5 = 0

. If

S (5, 0)

is a focus and

5 x = 9

is the corresponding directrix of this hyperbola, then

a^{2} - b^{2}

is equal to