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JEE Main

IMPORTANT

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The eccentric angle of a point $P$ lying in the first quadrant on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is $θ$ . If $O P$ makes an angle $ϕ$ with positive direction of $x$ -axis, then $θ - ϕ$ will be maximum when $θ =$

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Important Questions on Ellipse

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 14

Let

P

and

Q

be points of the ellipse

16 x^{2} + 25 y^{2} = 400

so that

P Q = \frac{96}{25}

P

and

Q

lie above the major axis. Circle drawn with

P Q

as diameter touches the major axis at positive focus, then the value of slope

' m'

P Q

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 15

If the reflection of the ellipse

\frac{{(x - 4)}^{2}}{16} + \frac{{(y - 3)}^{2}}{9} = 1

in the mirror line

x - y - 2 = 0

k_{1} x^{2} + k_{2} y^{2} - 160 x - 36 y + 292 = 0

, then

\frac{k_{1} + k_{2}}{5}

is equal to

MEDIUM

JEE Main

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 16

A point

P

moves on

x y -

plane such that

P S + P S^{'} = 4

, where

S (K, 0)

and

S^{'} (- K, 0),

then which of the following is not true about the locus of

P ?

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 17

The ratio of the area enclosed by the locus of the midpoint of

P S

and area of the ellipse is (

P

be any point on the ellipse and

S

is its focus)

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 18

Number of integral values of

α

for which the point

(7 - \frac{5}{4} α, α)

lies inside the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 19

Coordinates of the vertices

B

and

C

of a triangle

A B C

are

(2, 0)

and

(8, 0)

, respectively. The vertex

A

is varying in such a way that

4 \tan \frac{B}{2} \cdot \tan \frac{C}{2} = 1 .

Then locus of

A

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 20

P Q

and

Q R

are two focal chords of an ellipse and the eccentric angles of

P, Q

and

R

are

2 α, 2 β

and

2 γ

respectively, then

\tan β \tan γ

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 6 - Ellipse>DPP>Q 21

In triangle $A B C, a = 4$ and $b = c = 2 \sqrt{2}$ . A point $P$ moves within the triangle such that the square of its distance from $B C$ is half the area of rectangle contained by its distances from the other two sides. If $D$ is the centre of locus of $P$ , then

The eccentric angle of a point P lying in the first quadrant on the ellipse x2a2+y2b2=1 is θ. If OP makes an angle ϕ with positive direction of x-axis, then θ-ϕ will be maximum when θ=

Important Questions on Ellipse

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The eccentric angle of a point $P$ lying in the first quadrant on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is $θ$ . If $O P$ makes an angle $ϕ$ with positive direction of $x$ -axis, then $θ - ϕ$ will be maximum when $θ =$