Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 15

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IMPORTANT

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A hyperbola passing through a focus of the ellipse $\frac{x^{2}}{169} + \frac{y^{2}}{25} = 1$ its transverse and conjugate axes coincide respectively, with the major and minor axes of the ellipse. The product of eccentricities is $1$ . Then, the equation of the hyperbola is

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Important Questions on Hyperbola

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 16

The curve

5 x^{2} + 12 x y - 22 x - 12 y - 19 = 0

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 17

If the line

l x + m y - n = 0

will be a normal to the hyperbola, then

\frac{a^{2}}{l^{2}} - \frac{b^{2}}{m^{2}} = \frac{{(a^{2} + b^{2})}^{2}}{k}

, where

k

is equal to

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 18

If the chords of the hyperbola

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

touch the parabola

y^{2} = 4 a x

. Then, the locus of the middle points of these chords is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 19

The equation of the common tangent with positive slope to the parabola

y^{2} = 8 \sqrt{3} x

and the hyperbola

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

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 20

A hyperbola passes through

(3, 3)

and the length of its conjugate axis is

8

. The length of latus rectum is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 21

The value of

m

, for which the line

y = m x + 2

is a tangent to the hyperbola

4 x^{2} - 9 y^{2} = 36

, are

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 22

The eccentricity of the hyperbola with latus rectum

12

and semi-conjugate axis

2 \sqrt{3}

, is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 16 - Hyperbola>Entrances Gallery>Q 23

The equation to the common tangents to the two hyperbolas

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

and

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

are