If P C P ' and D C D ' form a pair of conjugate diameters of the ellipse x 2 a 2 + y 2 b 2 = 1 and R is any point on the circle x 2 + y 2 = c 2 , then

P R 2 + D R 2 + P ' R 2 + D ' R 2 = 2 a 2 + b 2 + 2 c 2

P R 2 - D R 2 - P ' R 2 - D ' R 2 = 2 a 2 - b 2 - 2 c 2

P R 2 + D R 2 + P ' R 2 + D ' R 2 = 2 a 2 - b 2 - 2 c 2

P R 2 + D R 2 + P ' R 2 + D ' R 2 = a 2 + b 2 + 2 c 2

P R 2 + D R 2 + P ' R 2 + D ' R 2 = 2 a 2 + b 2 + c 2

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JEE Advanced

IMPORTANT

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If $C P$ and $C D$ are conjugate semi-diameters of the ellipse, then $P D$ touches the ellipse

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Important Questions on Ellipse

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 58

α

and

β

are the angles subtended by the major axis of an ellipse at the extremities of a pair of conjugate diameters, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 59

P C P^{'}

and

D C D^{'}

form a pair of conjugate diameters of the ellipse

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

and

R

is any point on the circle

x^{2} + y^{2} = c^{2},

then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 60

P C P^{'}

and

D C D^{'}

are conjugate diameters of an ellipse

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

and

θ

is the eccentric angle of

P .

Then eccentric angle of the point where the circle

P P^{'} D

again cuts the ellipse

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 8

An ellipse is drawn by taking a diameter of the circle

(x - 1)^{2} + y^{2} = 1

as its semi-minor axis and a diameter of the circle

x^{2} + (y - 2)^{2} = 4

as semi-major axis. If the centre of the ellipse is at the origin and its axes are along the coordinate axes, then the equation of the ellipse is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 10

The equation of the ellipse whose axes are the axes of coordinates and which passes through the point

(- 3, 1)

and has eccentricity

\sqrt{\frac{2}{5}}

, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 11

The ellipse

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

is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point

(4, 0)

. Then, the equation of the ellipse is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 12

A focus of an ellipse is at the origin. The directrix is the line

x = 4

and the eccentricity is

\frac{1}{2}

, then the length of semi-major axis is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 13

In an ellipse, the distances between its foci is

6

and minor axis is

8

. Then, its eccentricity is

If CP and CD are conjugate semi-diameters of the ellipse, then PD touches the ellipse

Important Questions on Ellipse

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If $C P$ and $C D$ are conjugate semi-diameters of the ellipse, then $P D$ touches the ellipse