The chords of contact of perpendicular tangents to the ellipse x 2 a 2 + y 2 b 2 = 1 touch another fixed ellipse whose equation is

x 2 a 4 + y 2 b 4 = 1 a 2 + b 2

x 2 a 2 + y 2 b 2 = 1 2 a 2 + b 2

x 2 a 2 + y 2 b 2 = 2 ( a 2 - b 2 )

x 2 a 2 - y 2 b 2 = 2 3 a 2 - b 2

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IMPORTANT

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If the curve $x^{2} + 3 y^{2} = 9$ subtends an obtuse angle at the point $(2 α, α)$ , then a possible value of $α^{2}$ can be

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Important Questions on Ellipse

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 4

An ellipse has the point

(1, - 1)

and

(2, - 1)

as its foci and

x + y = 5

as one of its tangent, then the value of

a^{2} + b^{2}

, where

a, b

are the length of semi-major and semi-minor axis of ellipse respectively, is

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 5

An ellipse has foci at

(9, 20)

and

(49, 55)

in the

x y

-plane and tangent to it is the

x

-axis. The length of its major axis is

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 6

The maximum distance of the centre of the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ from the chord of contact of mutually perpendicular tangents of the ellipse is

MEDIUM

JEE Main

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 7

P_{1}

and

P_{2}

are lengths of the perpendiculars from the foci on the tangent to the ellipse and

P_{3}

and

P_{4}

are lengths of the perpendiculars from extremities of major axis and length of the perpendicular

P

from the centre of the ellipse on the same tangent, then

\frac{P_{1} P_{2} - P^{2}}{P_{3} P_{4} - P^{2}}

equals (where

e

is the eccentricity of the ellipse)

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 8

From the focus

(- 5, 0)

of the ellipse

\frac{x^{2}}{45} + \frac{y^{2}}{20} = 1

, a ray of light is sent which makes an angle

\cos^{- 1} (\frac{- 1}{\sqrt{5}})

with the positive direction of

x

-axis, upon reaching the ellipse surface, the ray is reflected from it. Slope of the reflected ray is

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 9

Let

5 x - 3 y = 8 \sqrt{2}

be normal at

P (\frac{5}{\sqrt{2}}, \frac{3}{\sqrt{2}})

to an ellipse

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

. If

M & M^{'}

are feet of perpendiculars from foci

S & S^{'}

, respectively on the tangent at

P

, then the point of intersection of

{SM}^{'}

and

S^{'} M

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 10

If the normals at

α, β, γ

and

δ

on an ellipse are concurrent, then the value of

(\sum_{} \cos α) (\sum_{} \sec α)

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 11

The chords of contact of perpendicular tangents to the ellipse

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

touch another fixed ellipse whose equation is

If the curve x2+3y2=9 subtends an obtuse angle at the point (2α, α), then a possible value of α2 can be

Important Questions on Ellipse

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If the curve $x^{2} + 3 y^{2} = 9$ subtends an obtuse angle at the point $(2 α, α)$ , then a possible value of $α^{2}$ can be