Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 3

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IMPORTANT

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The eccentric angles of the extremities of latus recta of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ are given by

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Important Questions on Ellipse

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 4

The eccentricity of the ellipse which meets the straight line

\frac{x}{7} + \frac{y}{2} = 1

on the axis of

x

and the straight line

\frac{x}{3} - \frac{y}{5} = 1

on the axis of

y

and whose axes lie along the axes of co-ordinate, is -

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 5

Let

P

be a variable point on the ellipse

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

with foci at

S

and

S^{'}

. If

A

be the area of triangle

P S S^{'}

, then the maximum value of

A

is :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 6

The length of common chord of the ellipse

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

and the circle

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

, is

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 7

If one end of a diameter of the ellipse

4 x^{2} + y^{2} = 16

is

(\sqrt{3}, 2)

, then the other end is:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 8

The line

x = {a t}^{2}

, meets the ellipse

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

in the real points, if

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 9

For the ellipse

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

, the equation of the diameter conjugate to

a x - b y = 0

is :

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 10

If the polar with respect to

y^{2} = 4 a x

touches the ellipse

\frac{x^{2}}{α^{2}} + \frac{y^{2}}{β^{2}} = 1,

the locus of its pole is

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 11

P

is a variable point on the ellipse

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

whose foci are

F_{1}

and

F_{2}

. The maximum area of

∆ P F_{1} F_{2}

is :