Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 18

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IMPORTANT

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The equation of the tangents to the ellipse $9 x^{2} + 16 y^{2} = 144$ which passes through the point $(2, 3)$ is

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Important Questions on Ellipse

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 19

If

F_{1}

and

F_{2}

are the foot of the perpendiculars from the foci

S_{1}

and

S_{2}

of an ellipse

\frac{x^{2}}{5} + \frac{y^{2}}{3} = 1

on the tangent at any point

P

on the ellipse, then

(S_{1} F_{1}) (S_{2} F_{2})

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 2>Q 1

S_{1}, S_{2}

are foci of an ellipse of major axis of length

10

units and

P

is any point on the ellipse such that the perimeter of the triangle

P S_{1} S_{2}

is

15 .

Then eccentricity of the ellipse is

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

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

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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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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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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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

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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