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

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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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Important Questions on Conic Section

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 39

For hyperbola

\frac{x^{2}}{\cos^{2} α} - \frac{y^{2}}{\sin^{2} α} = 1

which of the following remains constant with change in '

α

'?

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.4>Q 40

The locus of a point of the form

e^{t} + e^{- t}, e^{t} - e^{- t}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 41

If

e

and

e^{'}

be the eccentricities of a hyperbola and its conjugate, then

e^{2} + {(e^{'})}^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 42

If the eccentricity of a hyperbola is

\sqrt{3}

, then the eccentricity of its conjugate hyperbola is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 43

If the distance between the foci and the distance between the directrices of the hyperbola

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

are in the ratio

3 : 2,

then

a : b

is

=

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 44

Let

P Q

be a latus rectum of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{k^{2}}{b^{2}} = 1

and

O

be the centre. If

Δ O P Q

is an equilateral triangle and

e

is eccentricity of the hyperbola, then

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 45

The line

5 x + 12 y + 9 = 0

touches the hyperbola

x^{2} - 9 y^{2} = 9

at the point