Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 36

HARD

JEE Main/Advance

IMPORTANT

Earn 100

If the focal distance of an end of the minor axis of an ellipse, whose axes along the $x$ and $y$ axes respectively is $k$ and the distance between the foci is $2 h$ . Then the equation of the ellipse is

72.73% studentsanswered this correctly

Important Questions on Conic Section

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 38

The number of values of

c

, such that

y = 4 x + c

touches

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

, is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 39

The sum of the squares of the perpendiculars on any tangent to the ellipse

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

from two points on the minor axis each at a distance

\sqrt{a^{2} - b^{2}}

from the centre is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 40

The line

2 x + y = 3

cuts the ellipse

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

at

P

and

Q

. If $\theta$ be the angle between the normals at these points, then

\tan θ

is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 41

Number of points on the ellipse

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

from which pair of perpendicular tangents are drawn to the ellipse

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

, is

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 43

The equation of the chord of the ellipse

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

having the middle point at

(- 1, \frac{1}{2})

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 44

Pole of the line $x+4 y=5$ with respect to the ellipse

5 x^{2} + 4 y^{2} = 10

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 45

The locus of the mid points of the portion of the tangents to the ellipse

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

intercepted between the axes is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 46

A rod of given length moves such that its extremities lie on two fixed perpendicular lines. Any point (other than mid point) on the rod describes