EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 24 January 2023 Shift 1>Q 60

HARD

JEE Main

IMPORTANT

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Let $C$ be the largest circle centred at $(2, 0)$ and inscribed in the ellipse $\frac{x^{2}}{36} + \frac{y^{2}}{16} = 1$ . If $(1, α)$ lies on $C$ , then $10 α^{2}$ is equal to ______

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Important Questions on Ellipse

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 24 January 2023 Shift 1>Q 61

Let a tangent to the curve

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

intersect the coordinate axes at the points

A

and

B

. Then, the minimum length of the line segment

A B

is ______

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 31 January 2023 Shift 1>Q 62

If the maximum distance of normal to the ellipse

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

, from the origin is

1

, then the eccentricity of the ellipse is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 17 - Ellipse>JEE Main - 1 February 2023 Shift 2>Q 63

The line

x = 8

is the directrix of the ellipse

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

with the corresponding focus

(2, 0)

. If the tangent to

E

at the point

P

in the first quadrant passes through the point

(0, 4 \sqrt{3})

and intersects the

x

-axis at

Q

, then

{(3 P Q)}^{2}

is equal to _____ .