Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-3>Q 4

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Let the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ be reciprocal to that of the ellipse $x^{2} + 4 y^{2} = 4 .$ If the hyperbola passes through a focus of the ellipse, then

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Important Questions on Hyperbola

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-3>Q 5

Let

P (6, 3)

be a point on the hyperbola

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

If the normal at the point

P

intersects the

X

-axis at

(9, 0),

then the eccentricity of the hyperbola is

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-3>Q 6

Tangents are drawn to the hyperbola

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

, parallel to the straight line

2 x - y = 1

. The points of contact of the tangents on the hyperbola are

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-3>Q 7

The equation of the hyperbola, whose foci are

(- 2, 0)

and

(2, 0)

and eccentricity is

2

, is given by

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-4>Q 1

Find the points of intersection of the curves whose parametric equations are

x = t^{2} + 1, y = 2 t

and

x = 2 s, y = \frac{2}{s}

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-4>Q 2

The equations of the transverse and conjugate axes of a hyperbola are respectively

x + 2 y - 3 = 0, 2 x - y + 4 = 0

and their respective lengths are

\sqrt{2}

and

\frac{2}{\sqrt{3}}

. Then find the equation of the hyperbola.

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-4>Q 3

If

P

is any point common to the hyperbola

\frac{x^{2}}{16} - \frac{y^{2}}{25} = 1

and the circle having line segment joining its focii as diameter then find the sum of focal distances of point

P

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-4>Q 4

The transverse axis of a hyperbola is of length

2 a

and

a

vertex divides the segment of the axis between the centre and the corresponding focus in the ratio

2 : 1

. Find the equation of the hyperbola.

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Alpha Question Bank for Engineering: Mathematics>Chapter 19 - Hyperbola>Exercise-4>Q 5

If

x \cos α + y \sin α = p,

a variable chord of the hyperbola

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

subtends a right angle at the centre of the hyperbola, then the chords touch a fixed circle, find the radius of the circle.