EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 10th April 2019 Shift 1>Q 29

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JEE Main

IMPORTANT

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If the line $x - 2 y = 12$ is a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ at the point $(3, - \frac{9}{2})$ , then the length of the latus rectum of the ellipse is

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Important Questions on Ellipse

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 10th April 2019 Shift 2>Q 30

The tangent and normal to the ellipse

3 x^{2} + 5 y^{2} = 32

at the point

P (2, 2)

meet the

x

-axis at

Q

and

R

, respectively. Then the area (in sq. units) of the triangle

P Q R

is:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 12th April 2019 Shift 1>Q 31

If the normal to the ellipse

{3 x}^{2} + 4 y^{2} = 12

at a point

P

on it is parallel to the line,

2 x + y = 4

and the tangent to the ellipse at

P

passes through

Q (4,4)

then

P Q

is equal to:

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 12th April 2019 Shift 2>Q 32

An ellipse, with foci at

(0,2)

and

(0, - 2)

and minor axis of length

4

, passes through which of the following points?

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 12th January 2019 Shift 2>Q 33

Let

S

and

S^{'}

be the foci of an ellipse and

B

be any one of the extremities of its minor axis. If

Δ S^{'} B S

is a right angled triangle with right angle at

B

and area

(Δ S^{'} B S) = 8 sq . units

, then the length of a latus rectum of the ellipse is :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 8th April 2018>Q 34

Two sets

A

and

B

are as under:

A = \{(a, b) \in R \times R : |a - 5| < 1 and |b - 5| < 1\};

B = \{(a, b) \in R \times R : 4 {(a - 6)}^{2} + 9 {(b - 5)}^{2} \leq 36\} .

Then :

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 15th April 2018>Q 35

If

β

is one of the angles between the normals to the ellipse

x^{2} + 3 y^{2} = 9

at the points

(3 \cos θ, \sqrt{3} \sin θ)

and

(- 3 \sin θ, \sqrt{3} \cos θ); θ \in (0, \frac{π}{2})

; then

\frac{2 \cot β}{\sin 2 θ}

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 16th April 2018>Q 36

If the length of the latus rectum of an ellipse is

4

units and the distance between a focus and its nearest vertex on the major axis is

\frac{3}{2}

units, then its eccentricity is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 2nd April 2017>Q 37

The eccentricity of an ellipse whose centre is at the origin is

\frac{1}{2}

. If one of its directrices is

x = - 4

, then the equation of the normal to it at

(1, \frac{3}{2})

is: