Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 25

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

If the line $p x + q y = r$ intersects the ellipse $x^{2} + 4 y^{2} = 4$ in points, whose eccentric angles differ by $\frac{π}{3},$ then $r^{2}$ is equal to

50% studentsanswered this correctly

Important Questions on Conic Section

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 26

Minimum area of the triangle formed by any tangent to the ellipse

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

with the coordinate axes is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 27

Product of the perpendiculars drawn from the foci upon any tangent to the ellipse

3 x^{2} + 4 y^{2} = 12

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 28

The line

l x + m y + n = 0

is a normal to the ellipse

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

if

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 29

If the normal to the ellipse

\frac{x^{2}}{14} + \frac{y^{2}}{5} = 1

at the point

θ

intersects the curve again at the point

2 θ,

then cos

θ

is equal to

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.3>Q 30

The equation of the director circle of the ellipse

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

is given by

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 31

If

α

and

β

are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 32

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

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 33

If

P (θ)

and

Q (\frac{π}{2} + θ)

are two points on the ellipse

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

then locus of the mid-point of

P Q

is