Question

If angle between the asymptotes of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1is{45}^0$, then value of eccentricity e is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$2ta{n}^{-1}\frac{b}{a}={45}^0\Rightarrow \frac{b}{a}=tan{22.5}^0\Rightarrow \frac{a^2(e^2-1)}{a^2}={(\sqrt{2}-1)}^2\Rightarrow e^2-1=3-2\sqrt{2}\Rightarrow e=\sqrt{4-2\sqrt{2}}.$