Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 10

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If $e_{1}$ and $e_{2}$ are the eccentricities of the conic sections $16 x^{2} + 9 y^{2} = 144$ and $9 x^{2} - 16 y^{2} = 144,$ then

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Important Questions on Hyperbola

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Mathematics

IMPORTANT

Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 11

If the foci of the ellipse

\frac{x^{2}}{k^{2} a^{2}} + \frac{y^{2}}{a^{2}} = 1, (k > 1)

and hyperbola

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

coincides then

k = ?

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 12

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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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 13

The foci of the hyperbola

9 x^{2} - 16 y^{2} + 18 x + 32 y - 151 = 0

are

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 14

It two distinct tangents can be drawn from the point

(α, 2)

on different branches of the hyperbola

\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1,

then

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Mathematics

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 15

From a point

P (1, 2)

two tangents are drawn to a hyperbola

' H'

in which one tangent is drawn to each arm of the hyperbola. If the equations of asymptotes of hyperbola

H

are

\sqrt{3} x - y + 5 = 0

and

\sqrt{3} x + y - 1 = 0,

then eccentricity of

' H'

is

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Mathematics

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 16

If

θ

is the angle between the asymptotes of the hyperbola

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

with eccentricity

e,

then

\sec \frac{θ}{2}

can be-

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 17

If

m_{1}

and

m_{2}

are the slopes of the tangents to the hyperbola

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

which passes through the point

(6, 2),

then

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Mathematics Crash Course BITSAT>Chapter 12 - Hyperbola>Exercise 1>Q 18

The equation of tangents to the hyperbola

3 x^{2} - 2 y^{2} = 6

, which is perpendicular to the line

x - 3 y = 3

, are