Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.1>Q 5

MEDIUM

JEE Main/Advanced

IMPORTANT

Earn 100

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:

50% studentsanswered this correctly

Important Questions on Ellipse

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.1>Q 6

The length of the major axis of the ellipse

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

is three times the length of minor axis, it eccentricity is :

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.1>Q 1

Find the latus rectum, eccentricity, coordinates of the foci, coordinates of the vertices, the length of the axes and the centre of the ellipse

4 x^{2} + 9 y^{2} - 8 x - 36 y + 4 = 0

.

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.1>Q 2

The distance between the foci of an ellipse is

10

and its latus rectum is

15;

find its equation referred to its axes as axes of coordinates.

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.1>Q 3

Find the equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point

(2, - 3)

one focus at

(3, - 3)

and one vertex at

(4, - 3)

.

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.1>Q 4

Find the equation of the ellipse whose foci are

(2, 3)

,

(- 2, 3)

and whose semi-minor axis is

\sqrt{5}

.

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.1>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 :

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.2>Q 1

If the normal at one end of the latusrectum of an ellipse

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

passes through the one end of the minor axis, then

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 6 - Ellipse>INTRODUCTORY EXERCISE 6.2>Q 2

If the normal at point

P

on the ellipse

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

meets the axes in

R

and

S

respectively, then

P R : R S

is equal to