Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.3>Q 9

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IMPORTANT

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The locus of the point of intersection of the perpendicular tangents to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ 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>INTRODUCTORY EXERCISE 6.3>Q 10

The area of the parallelogram inscribed in the ellipse

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

whose diagonals are the conjugate diameters of the ellipse is given by :

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.3>Q 1

Find the locus of the vertices of equilateral triangle circumscribing the ellipse

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

.

EASY

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IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.3>Q 2

A tangent to the ellipse

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

meets the ellipse

x^{2} + 2 y^{2} = 6

at

P & Q

. Prove that the tangents at

P & Q

of the ellipse

x^{2} + 2 y^{2} = 6

are at right angles.

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.3>Q 3

Find the locus of the mid-point of chords of the ellipse

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

passing through the point

(2 a, 0)

.

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.3>Q 4

Obtain the locus of poles of tangents to the ellipse

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

with respect to concentric ellipse

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

.

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JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.3>Q 5

Find the locus of the point, the chord of contact of the tangents drawn from which to the ellipse

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

touches the circle

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

, where

c < b < a

.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.3>Q 6

Find the centre and eccentricity of the ellipse.

4 {(x - 2 y + 1)}^{2} + 9 {(2 x + y + 2)}^{2} = 5

.

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>EXERCISE ON LEVEL-I>Q 32

A ray emanating from the point

(- 4, 0)

is incident on the ellipse

9 x^{2} + 25 y^{2} = 225

at the point

P

with abscissa

3 .

Find the equation of the reflected ray after first reflection.