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

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IMPORTANT

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$P C P^{'}$ 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

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Important Questions on Ellipse

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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

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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

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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

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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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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

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 14

Area of the greatest rectangle that can be inscribed in the ellipse

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

is

HARD

JEE Advanced

IMPORTANT

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

An ellipse has

O B

as semi-minor axis,

F

and

F^{'}

its foci and the

∠ F B F^{'}

is a right angle. Then, the eccentricity of the ellipse is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 16

The eccentricity of an ellipse with its centre at the origin is

\frac{1}{2}

. If one of the directrices is

x = 4,

then the equation of the ellipse is