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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

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Important Questions on Ellipse

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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

(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

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.2>Q 4

F_{1}

and

F_{2}

are the foot of the perpendiculars from the foci

S_{1}

and

S_{2}

of an ellipse

\frac{x^{2}}{5} + \frac{y^{2}}{3} = 1

on the tangent at any point

P

on the ellipse, then

(S_{1} F_{1}) (S_{2} F_{2})

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.2>Q 5

The slope of a common tangent to the ellipse

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

and a concentric circle of radius

r

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.2>Q 6

p

and

p^{'}

denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length

a

, respectively on a tangent to the ellipse and

r

denotes the focal distance of the point, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.2>Q 7

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>Work Book Exercise 15.3>Q 1

Chords of an ellipse are drawn through the positive end of the minor axis. Then, their midpoint lies on

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.3>Q 2

The area of rectangle formed by the perpendiculars from the centre of an ellipse to the tangent and normal at the point, whose eccentric angle is

π / 4

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Work Book Exercise 15.3>Q 3

If the chords of contact of tangent from two points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

to the ellipse

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

are at right angles, then

\frac{x_{1} x_{2}}{y_{1} y_{2}}

is equal to

If PSQ is a focal chord of the ellipse x2a2+y2b2=1, a>b, then the harmonic mean of SP and SQ is

Important Questions on Ellipse

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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