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

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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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Important Questions on Ellipse

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JEE Main/Advanced

IMPORTANT

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 :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 12

An ellipse slides between two perpendicular straight lines. Then the locus of its centre is-

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 13

The parametric representation of a point on the ellipse whose foci are

(- 1,0)

and

(7, 0)

and eccentricity

\frac{1}{2}

is

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 14

The locus of

P

satisfying the condition

|P F_{1}| + |P F_{2}| = 10; F_{1} \equiv (1, 2); F_{2} \equiv (12, 2)

is :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 15

S and T are the foci of the ellipse $(\frac{x^{2}}{a^{2}}) + (\frac{y^{2}}{b^{2}}) = 1$ and B is an end of the minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse is:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 16

If

C F

is the perpendicular from the centre

C

of the ellipse

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

on the tangent at any point

P

and

G

is the point when the normal at

P

meets the major axis, then

C F \cdot P G =

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>Multiple Choice I>Q 17

The distance of the point at angle

θ

on the ellipse

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

from a focus is