EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 8th January 2020 Shift 2>Q 15

MEDIUM

JEE Main

IMPORTANT

Earn 100

If a hyperbola passes through the point $P (10, 16)$ , and it has vertices at $(\pm 6, 0)$ , then the equation of the normal to it at $P$ , is.

50% studentsanswered this correctly

Important Questions on Hyperbola

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 9th April 2019 Shift 1>Q 16

If the line

y = m x + 7 \sqrt{3}

is normal to the hyperbola

\frac{x^{2}}{24} - \frac{y^{2}}{18} = 1

, then a value of

m

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 9th January 2019 Shift 1>Q 17

Let

0 < θ < \frac{π}{2} .

If the eccentricity of the hyperbola

\frac{x^{2}}{\cos^{2} θ} - \frac{y^{2}}{\sin^{2} θ} = 1

is greater than

2,

then the length of its latus rectum lies in the interval:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 9th January 2019 Shift 2>Q 18

A hyperbola has its centre at the origin, passes through the point

(4, 2)

and has transverse axis of length

4

along the

x - a x i s .

Then the eccentricity of the hyperbola is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 8th April 2019 Shift 2>Q 19

If the eccentricity of the standard hyperbola passing through the point

(4,6)

is

2,

then the equation of the tangent to the hyperbola at

(4,6)

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 10th April 2019 Shift 1>Q 20

If a directrix of a hyperbola centered at the origin and passing through the point

(4, - 2 \sqrt{3})

is

5 x = 4 \sqrt{5}

and its eccentricity is

e

, then:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Hyperbola>JEE Main - 10th April 2019 Shift 2>Q 21

If

5 x + 9 = 0

is the directrix of the hyperbola

16 x^{2} - 9 y^{2} = 144,

then its corresponding focus is:

EASY

JEE Main

IMPORTANT

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

The equation of a tangent to the hyperbola,

4 x^{2} - 5 y^{2} = 20,

parallel to the line

x - y = 2,

is

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: