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

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Product of the perpendiculars drawn from the foci upon any tangent to the ellipse $3 x^{2} + 4 y^{2} = 12$ is

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Important Questions on Conic Section

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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

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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

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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

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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

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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

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 34

A B

is a diameter of

x^{2} + 9 y^{2} = 25

. The eccentric angle of

A

is

π / 6

. Then find the eccentric angle of other end of diameter

A

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 35

In the ellipse

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

and

3 y + 2 x = 0

are a pair of conjugate diameters. Then the eccentricity of the ellipse is