Question

If the latus rectum of a hyperbola through one focus subtends 60° at the other focus then its eccentricity e =

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$Given,\angle S{S}^{\prime }L={30}^{\circ }$

$Given,\angle S{S}^{\prime }L={30}^{\circ }\therefore tan{30}^{\circ }=\frac{SL}{S{S}^{\prime }}\Rightarrow \frac{1}{\sqrt{3}}=\frac{b^{2}a}{2ae}\Rightarrow \frac{1}{\sqrt{3}}=\frac{a^2(e^2-1)}{2a^{2}e}\Rightarrow \sqrt{3}{e}^2-2e-\sqrt{3}=0\Rightarrow e=\sqrt{3}$