EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 4 September 2020 Shift 1>Q 15

MEDIUM

JEE Main

IMPORTANT

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Let $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b)$ be a given ellipse, length of whose latus rectum is $10$ . If its eccentricity is the maximum value of the function, $ϕ (t) = \frac{5}{12} + t - t^{2}$ , then $a^{2} + b^{2}$ 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 - 4 September 2020 Shift 2>Q 16

Let

x = 4

be a directrix to an ellipse whose centre is at the origin and its eccentricity is

\frac{1}{2} .

If

P (1, β), β > 0

is a point on this ellipse, then the equation of the normal to it at

P

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 5 September 2020 Shift 1>Q 17

If the co-ordinates of two points

A

and

B

are

(\sqrt{7}, 0)

and

(- \sqrt{7}, 0)

respectively and

P

is any point on the conic,

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

then

P A + P B

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 5 September 2020 Shift 1>Q 18

If the point

P

on the curve,

4 x^{2} + 5 y^{2} = 20

is farthest from the point

Q (0, - 4)

, then

P Q^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 6 September 2020 Shift 1>Q 19

Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse,

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

from any of its foci?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 6 September 2020 Shift 2>Q 20

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity

e

of the ellipse satisfies :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 7th January 2020 Shift 1>Q 21

If the distance between the foci of an ellipse is

6

and the distance between its directrix is

12,

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 - 7th January 2020 Shift 2>Q 22

If

3 x + 4 y = 12 \sqrt{2}

is a tangent o the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{9} = 1

for some

a \in R,

then the distance between the foci of the ellipse is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 8th January 2020 Shift 1>Q 23

Let the line

y = m x

and the ellipse

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

intersect at a point

P

in the first quadrant. If the normal to this ellipse at

P

meets the co-ordinate axes at

(- \frac{1}{3 \sqrt{2}}, 0)

and

(0, β)

, then

β

is equal to