Question

If the angle between the asymptotes of a hyperbola is $2\theta$ then eccentricity of hyperbola =?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Angle between the asymptotes=$2\theta$

Transverse axis acts as an angle bisector of asymptotes

Vertex of the hyperpola is (a,0)

Vertex of conjugate hyperpola is (b,0)

In $\Delta OAB$

$tan\theta =\frac{b}{a}$

We know, eccentricity of hyperpola $e^2=1+\frac{b^2}{a^2}$

$e^2=1+ta{n}^2\theta \{\frac{b}{a}=tan\theta \}$

$e^2=se{c}^2\theta$

$e=sec\theta$

If $2\theta$ is the angle between the asymptotes,

Eccentricity of the hyperpola=$sec\theta$