Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

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Equation of hyperbola passing through origin and whose asymptotes are $3 x + 4 y = 5$ and $4 x + 3 y = 5,$ is-

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Important Questions on Hyperbola

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The equations of the asymptotes of the hyperbola

x y + 3 x - 2 y - 10 = 0

are

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The combined equation of the asymptotes of the hyperbola

2 x^{2} + 5 x y + 2 y^{2} + 4 x + 5 y = 0

is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

Show that the angle between the two asymptotes of a hyperbola

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

is

2 \tan^{- 1} (\frac{b}{a})

or

2 \sec^{- 1} (e)

.

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The equation of the asymptotes of the hyperbola

2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0

is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The equations of the asymptotes of the hyperbola

2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0

are

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The angle between the two asymptotes of the hyperbola

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

is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The angle between the asymptotes of the hyperbola

x^{2} + 2 x y - 3 y^{2} + x + 7 y + 9 = 0

is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The eccentricity of the hyperbola whose asymptotes are

3 x + 4 y = 2

and

4 x - 3 y + 5 = 0

, is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

If the

3 x - 4 y + 1 = 0

and

4 x + 3 y - 3 = 0

are asymptotes of a hyperbola, then its eccentricity is.

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The angle between the asymptotes of a hyperbola is

30 ° .

The eccentricity of the hyperbola is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The combined equation of the asymptotes of the hyperbola

2 x^{2} + 5 x y + 2 y^{2} + 4 x + 5 y = 0

is

HARD

Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

A hyperbola has the asymptotes

x + 2 y = 3

and

x - y = 0

and passes through (2, 1). Its centre is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The product of perpendiculars drawn from any point of a hyperbola to its asymptotes is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

Eccentricity of hyperbola whose asymptotes are

3 x - 4 y = 7 a n d 4 x + 3 y = 8

, is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

If

e

is the eccentricity of

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

and

θ

be the angle between the asymptotes. then

\frac{\sec θ}{2}

is equal to

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The equation of the asymptotes of the hyperbola

3 x^{2} + 4 y^{2} + 8 x y - 8 x - 4 y - 6 = 0

is

HARD

Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The foci of a hyperbola lie on the line

y = x

and one of it's asymptotes is the line

y = 2 x

. If the given hyperbola passes through the point

(3, 4)

, then the equation of the hyperbola, is equal to

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

Asymptotes of Hyperbola

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

are .....

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

The product of the lengths of perpendicular drawn from any point on the hyperbola

x^{2} - 2 y^{2} - 2 = 0

to its asymptotes, is

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Mathematics>Coordinate Geometry>Hyperbola>Asymptotes of a Hyperbola

Cotyledons are also called-