Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Entrances Gallery>Q 35

HARD

JEE Advanced

IMPORTANT

Earn 100

Area of a triangle formed by tangent and normal to the curve $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ at $P (\frac{a}{\sqrt{2}}, \frac{b}{\sqrt{2}})$ with the $X$ -axis is

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Important Questions on Ellipse

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.1>Q 1

If the eccentricity of the ellipse

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

is

\frac{1}{\sqrt{6}}

, then the length of latus rectum is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.1>Q 2

If

S_{1}, S_{2}

are foci of an ellipse of major axis of length

10

units and

P

is any point on the ellipse such that perimeter of

Δ P S_{↑} S_{2}

is

15

. Then, eccentricity of the ellipse is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.1>Q 3

The length of major axis of the ellipse

{(5 x - 10)}^{2} + {(5 y + 15)}^{2} = \frac{(3 x - 4 y + 7)^{2}}{4}

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.1>Q 4

If

S

and

S^{'}

are the foci of the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

and

P

is any point on it, then range of value of

S P \cdot S^{'} P

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.1>Q 5

The equation of the ellipse, whose focus is

(1, - 1)

the directrix is the line

x - y = 3

and eccentricity is

\frac{1}{2},

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.2>Q 1

A tangent to the ellipse

4 x^{2} + 9 y^{2} = 36

is cut by the tangent at the extremities of the major axis at

T

and

T^{'}

. The circle on

T T^{'}

as diameter passes through the point

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.2>Q 2

If

P S Q

is a focal chord of the ellipse

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

a > b,

then the harmonic mean of

S P

and

S Q

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.2>Q 3

Tangent is drawn to the ellipse

\frac{x^{2}}{27} + y^{2} = 1

at

(3 \sqrt{3} \cos θ, \sin θ),

where

θ \in (0, \frac{π}{2}),

then the value of

θ

such that sum of intercepts on axes made by the tangent is minimum, is