EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 26 June 2022 Shift 2>Q 49

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JEE Main

IMPORTANT

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If $m$ is the slope of a common tangent to the curves $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ and $x^{2} + y^{2} = 12$ , then $12 m^{2}$ 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 - 26 June 2022 Shift 2>Q 50

The locus of the mid-point of the line segment joining the point

(4, 3)

and the points on the ellipse

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

is an ellipse with eccentricity

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 27 June 2022 Shift 1>Q 51

Let the eccentricity of an ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, a > b

, be

\frac{1}{4}

. If this ellipse passes through the point

(- 4 \sqrt{\frac{2}{5}}, 3)

, then

a^{2} + b^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 29 June 2022 Shift 1>Q 52

Let

P Q

be a focal chord of the parabola

y^{2} = 4 x

such that it subtends an angle of

\frac{π}{2}

at the point

(3, 0)

. Let the line segment

P Q

be also a focal chord of the ellipse

E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, a^{2} > b^{2}

. If

e

is the eccentricity of the ellipse

E

, then the value of

\frac{1}{e^{2}}

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 25 July 2022 Shift 2>Q 53

If the ellipse

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

meets the line

\frac{x}{7} + \frac{y}{2 \sqrt{6}} = 1

on the

x

-axis and the line

\frac{x}{7} - \frac{y}{2 \sqrt{6}} = 1

on the

y

-axis, then the eccentricity of the ellipse is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 26 July 2022 Shift 2>Q 54

The acute angle between the pair of tangents drawn to the ellipse

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

from the point

(1, 3)

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 27 July 2022 Shift 1>Q 55

If the length of the latus rectum of the ellipse

x^{2} + 4 y^{2} + 2 x + 8 y - λ = 0

is

4

, and

l

is the length of its major axis, then

λ + l

is equal to _____.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 27 July 2022 Shift 2>Q 56

A common tangent

T

to the curves

C_{1} : \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1

and

C_{2} : \frac{x^{2}}{42} - \frac{y^{2}}{143} = 1

does not pass through the fourth quadrant. If

T

touches

C_{1}

at

(x_{1}, y_{1})

and

C_{2}

at

(x_{2}, y_{2})

, then

|2 x_{1} + x_{2}|

is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 28 July 2022 Shift 2>Q 57

Let the tangents at the points

P

and

Q

on the ellipse

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

meet at the point

R (\sqrt{2}, 2 \sqrt{2} - 2)

. If

S

is the focus of the ellipse on its negative major axis, then

S P^{2} + S Q^{2}

is equal to