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

HARD

JEE Advanced

IMPORTANT

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The point at shortest distance from the line $x + y = 7$ and lying on an ellipse $x^{2} + 2 y^{2} = 6$ , has coordinates

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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 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?

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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

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 20

If the straight line

y = 4 x + c

is a tangent to the ellipse

\frac{x^{2}}{8} + \frac{y^{2}}{4} = 1,

then

c

will be equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 21

From point

P (8, 27)

tangents

P Q

and

P R

are drawn to the ellipse

\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1 .

Then, angle subtended by

Q R

at origin is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 22

Equation of the tangent to the ellipse

\frac{x^{2}}{4} + \frac{y^{2}}{3} = 1

perpendicular to the line

2 x + y + 7 = 0,

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 23

Equation of the tangents to the ellipse

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

which are parallel to the line

x + y + 1 = 0

, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 24

If from a point

P

tangents

P Q

and

P R

are drawn to the ellipse

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

so that equation of

Q R

is

x + 3 y = 1,

then coordinates of

P

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 15 - Ellipse>Target Exercises>Q 25

The angle between pair of tangents drawn to the ellipse

3 x^{2} + 2 y^{2} = 5

from the points

(1, 2),

is