Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 2

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JEE Main

IMPORTANT

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Let $S$ and $S^{'}$ be two foci of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ . If a circle described on $S S^{'}$ as diameter intersects the ellipse in real and distinct points, then the eccentricity $e$ of the ellipse satisfies

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Important Questions on Ellipse

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 3

The centre of the ellipse

4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 4

The centre of the ellipse

\frac{(x + y - 3)^{2}}{9} + \frac{(x - y + 1)^{2}}{16} = 1

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 5

B

is an extremity of the minor axis of an ellipse whose foci are

S

and

S^{'}

. If

∠ S B S^{'}

is a right angle, then the eccentricity of the ellipse is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 6

If a bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on bar marked on the bar describes a/an

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 7

The point of intersection of the tangents at the point

P

on the ellipse

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

and its corresponding point

Q

on the auxiliary circle meet on the line

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 8

If

α - β =

constant, then the locus of the point of intersection of tangents at

P (a \cos α, b \sin α)

and

Q (a \cos β, b \sin β)

to the ellipse

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

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 9

If the tangent at the point

(4 \cos θ, \frac{16}{\sqrt{11}} \sin θ)

to the ellipse

16 x^{2} + 11 y^{2} = 256

is also a tangent to the circle

x^{2} + y^{2} - 2 x = 15

, then the value of

θ

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 10

If the length of portion of the major axis intercepted between the tangent and normal at a point

P (a \cos θ, b \sin θ)

on the ellipse

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

is equal to the length of semi-major axis, then eccentricity of the ellipse is