Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 2

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Mathematics

IMPORTANT

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The distance between the directrices of the ellipse $(4 x - 8)^{2} + 16 y^{2} = (x + \sqrt{3} y + 10)^{2}$ is

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Important Questions on Ellipse

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 3

A chord is drawn passing through

P (2, 2)

on the ellipse

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

such that it intersects the ellipse at points

A and B

. Then the maximum value of

P A \cdot P B

is equal to

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 4

A series of concentric ellipses

E_{1}, E_{2}, \dots \dots, E_{n}

are drawn such that

E_{n}

touches the extremities of the major axis of

E_{n - 1}

and the foci of

{\dot{E}}_{n}

coincide with the extremities of minor axis of

E_{n - 1} .

If the eccentricity of the ellipses is independent of

n,

then the value of the eccentricity, is

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 5

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

is

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 6

If the normal at any point

P

on the ellipse

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

meets the auxiliary circle at

Q

and

R

, such that

∠ Q O R = 90 °

, where

O

is the center of the ellipse, then

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 7

If the normal at any point

P

of the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

meets the coordinate axes at

M

and

N

, respectively, then

P M : P N

equals to

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 8

At a point

P

on the ellipse

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

tangent

P Q

is drawn. If the point

Q

be at a distance

\frac{1}{p}

from the point

P

, where

‘ p ’

is distance of the tangent from the origin, then the locus of the point

Q

is

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 9

P & Q

are corresponding points on the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

, and the auxiliary circle respectively. The normal at

P

to the ellipse meets

C Q

in

R

where

C

is centre of the ellipse. Then

ℓ (C R)

is

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 10 - Ellipse>Exercise 1>Q 10

From a point

P

perpendicular tangents

PQ

and

PR

are drawn to ellipse

x^{2} + 4 y^{2} = 4

, then locus of circumcentre of the triangle

PQR

is