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

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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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Important Questions on Conic Section

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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

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 46

The tangent at point

(2 \sec θ, 3 \tan θ)

of the hyperbola

\frac{x^{2}}{4} - \frac{y^{2}}{9} = 1

is parallel to

3 x - 4 y + 4 = 0

, then the value of

θ

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 47

The equation

2 x^{2} + 3 y^{2} - 8 x - 18 y + 35 = k

represents

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 48

The equation of a tangent to the hyperbola

16 x^{2} - 25 y^{2} - 96 x + 100 y - 356 = 0

, which makes an angle

\frac{π}{4}

with the transverse axis, is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 49

The locus of a point

P (α, β)

moving under the condition that the line

y = α x + β

is a tangent to the hyperbola

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

, is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.5>Q 50

If

x = 9

is the chord of contact of the hyperbola

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

then the equation of the corresponding pair of tangents is -

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.6>Q 51

The equation of the hyperbola whose asymptotes are the straight lines

3 x - 4 y + 7 = 0

and

4 x + 3 y + 1 = 0

and which passes through the origin, is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Application of Derivatives>Assignment>Q 1

If the line

a x + b y + c = 0

is a normal to the curve

x y = 2,

then