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 act as an angle bisector of asymptotes

Vertex of the hyperbola is (a,0)

Vertex of conjugate hyperbola is (b,0)

In $\Delta OAB$

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

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

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

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

$e=sec\theta$

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

Eccentricity of the hyperbola=$sec\theta$