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

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The equation of the director circle of the ellipse $4 x^{2} + 9 y^{2} = 36,$ is given by

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Important Questions on Conic Section

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

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 36

If the polar with respect to

y^{2} = 4 a x

touches the ellipse

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

the locus of its pole is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 37

The equation of the hyperbola whose directrix is

2 x + y = 1,

corresponding focus is

(1, 2)

and eccentricity

\sqrt{3},

is given by

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 38

If the foci of the ellipse

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

and the hyperbola

\frac{x^{2}}{144} - \frac{y^{2}}{81} = \frac{1}{25}

coincide, then the value of

b^{2}

is