Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.6>Q 57

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The point of intersection of tangents at $t_{1}$ and $t_{2}$ to the hyperbola $x y = c^{2}$ 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 13.6>Q 58

A rectangular hyperbola whose centre is

C

is cut by any circle of radius

r

in four points

P, Q, R, S .

The value of

C P^{2} + C Q^{2} + C R^{2} + C S^{2}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.6>Q 59

The equation to the chord joining two points

(x_{1}, y_{1})

and

(x_{2}, y_{2})

on the rectangular hyperbola

x y = c^{2}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>EXERCISE 13.6>Q 60

The equation of the common tangent to the curves

y^{2} = 8 x

and

x y = - 1,

is

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 1

Find the equation of the parabola with vertex at the origin and focus at

(0, - 3) .

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 2

Find the

c o

-ordinates of the foci and the vertices of the ellipse

x^{2} + 4 y^{2} = 16 .

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 3

If

20 x^{2} - 4 y^{2} = 80

represents the equation of a hyperbola, then find the length of its latus rectum.

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 4

Find the length of the latus rectum of the parabola

x^{2} = - 16 y .

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Gamma Question Bank for Engineering Mathematics>Chapter 14 - Conic Section>Assignment>Q 5

If

\frac{x^{2}}{64} + \frac{y^{2}}{36} = 1

represents the equation of an ellipse, then find the distance between its foci.