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

HARD

JEE Advanced

IMPORTANT

Earn 100

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 $Δ A B C$

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 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

is

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,

if

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

then the value of eccentricity is

HARD

JEE Advanced

IMPORTANT

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

Number of points on the ellipse

\frac{x^{2}}{50} + \frac{y^{2}}{20} = 1,

from where pair of perpendicular tangents are drawn to the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1,

are

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 16

Let

(α, β)

be a point from which two perpendicular tangents can be drawn to the ellipse

4 x^{2} + 5 y^{2} = 20

. If

F = 4 α + 3 β,

then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 17

The point at shortest distance from the line

x + y = 7

and lying on an ellipse

x^{2} + 2 y^{2} = 6

, has coordinates

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 18

If the equation of the ellipse is

2 x^{2} + 3 y^{2} - 8 x + 6 y + 5 = 0,

then which of the following is true?

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 19

Locus of all such points from where the tangents drawn to the ellipse

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

are always inclined at

45 °,

is