EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 9th April 2019 Shift 2>Q 26

HARD

JEE Main

IMPORTANT

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If the tangent to the parabola $y^{2} = x$ at a point $(α, β), (β > 0)$ is also a tangent to the ellipse, $x^{2} + 2 y^{2} = 1$ then $α$ is equal to:

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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 - 8th April 2019 Shift 1>Q 27

Let

O (0,0)

and

A (0,1)

be two fixed points. Then, the locus of a point

P

such that the perimeter of

Δ A O P

is

4

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 8th April 2019 Shift 2>Q 28

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at

(0,5 \sqrt{3}),

then the length of its latus rectum is:

MEDIUM

JEE Main

IMPORTANT

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

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

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?

MEDIUM

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 :