If P is any point lying on the ellipse x 2 a 2 + y 2 b 2 = 1 , whose foci are S and S ' . Let ∠ P S S ' = α and ∠ P S ' S = β , then which of the following is/are true?

tan α 2 tan β 2 = a 2 - b 2 b 2 a - a 2 - b 2

P S + P S ' = 2 α , if α > β

P S + P S ' = 2 β , if α > β

tan α 2 tan β 2 = 1 + e 1 - e

If P is any point lying on the ellipse x 2 a 2 + y 2 b 2 = 1 , whose foci are S and S ' . Let ∠ P S S ' = α and ∠ P S ' S = β , then which of the following is/are true?

tan α 2 tan β 2 = a 2 - b 2 b 2 a - a 2 - b 2

If α and β are the eccentric angles of the extremities of a focal chord of an ellipse x 2 a 2 + y 2 b 2 = 1 , then the eccentricity of the ellipse is

sin α + sin β sin ( α + β )

cos α + cos β cos ( α - β )

sin α - sin β sin ( α - β )

cos α - cos β cos ( α - β )

sin α - sin β sin ( α + β )

Three points A , B and C are taken on the ellipse x 2 a 2 + y 2 b 2 = 1 with eccentric angles θ , θ + α and θ + 2 α , then the area of the Δ A B C

has maximum value 3 3 4 a b sq. unit.

maximum value of area is 3 4 a b sq unit.

has maximum value a b 4 sq. unit.

HARD

JEE Advanced

IMPORTANT

Earn 100

If $P$ is any point lying on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ , whose foci are $S$ and $S^{'}$ . Let $∠ P S S^{'} = α$ and $∠ P S^{'} S = β$ , then which of the following is/are true?

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Important Questions on Ellipse

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 7

(a \cos α, b \sin α), (a \cos β, b \sin β)

are the endpoints of a focal chord of an ellipse, then which of the following is correct?

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 8

If the ellipse

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

is inscribed in a rectangle whose length to breadth ratio is

2 : 1,

then the area of the rectangle is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 9

A circle has the same centre as an ellipse and passes through the foci

F_{1}

and

F_{2}

of the ellipse, such that the two curves intersect in

4

points. Let

P

be any one of their points of intersection. If the major axis of the ellipse is

17

and the area of the

Δ P F_{1} F_{2}

30,

then the distance between the foci is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 10

α

and

β

are the eccentric angles of the extremities of a focal chord of an ellipse

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

, then the eccentricity of the ellipse is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 11

Three points $A, B$ and $C$ are taken on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ with eccentric angles $θ, θ + α$ and $θ + 2 α,$ then the area of the $Δ A B C$

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 12

The equation of the line passing through the centre and bisecting the chord

7 x + y - 1 = 0

of the ellipse

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

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 13

Tangents are drawn to the ellipse

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

and the circle

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

at the points, where a common ordinate cuts them (on the same side of the

X

-axis). Then, the greatest acute angle between these tangents is given by

HARD

JEE Advanced

IMPORTANT

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

Let

P_{i}

and

P_{i}^{'}

be the foot of the perpendiculars drawn from foci

S, S^{'}

on a tangent

T_{i}

to an ellipse whose length of semi-major axis is

20,

\sum_{i = 1}^{10} (S P_{i}) (S^{'} P_{i}^{'}) = 2560,

then the value of eccentricity is

If P is any point lying on the ellipse x2a2+y2b2=1, whose foci are S and S'. Let ∠PSS'=α and ∠PS'S=β, then which of the following is/are true?

Important Questions on Ellipse

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If $P$ is any point lying on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ , whose foci are $S$ and $S^{'}$ . Let $∠ P S S^{'} = α$ and $∠ P S^{'} S = β$ , then which of the following is/are true?