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 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

The semi latus rectum of an ellipse is

50% studentsanswered this correctly

Important Questions on Ellipse

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 4

If the ellipse

\frac{x^{2}}{a^{2} - 7} + \frac{y^{2}}{13 - 5 a} = 1

is inscribed in a square of side length

\sqrt{2} a,

then

a

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 5

A parabola is drawn with focus is at one of the foci of the ellipse

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

(where,

a > b

) and directrix passing through the other focus and perpendicular to the major axes of the ellipse. If latus rectum of the ellipse and the parabola are same, 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 6

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?

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 $Δ A B C$

The semi latus rectum of an ellipse is

Important Questions on Ellipse

Learn and Prepare for any exam you want !