Question

If the latus rectum through one focus subtends a right angle at the farther vertex of the hyperbola then its
eccentricity is

• A. 4
• B.
• C. 2
• D.

Answer 1

The correct option is C 2

$\therefore \angle S{A}^{\prime }L={45}^{\circ }$

$tan{45}^{\circ }=\frac{SL}{A^{\prime }S}\Rightarrow 1=\frac{b^2}{a(a+ae)}$
$\Rightarrow 1=\frac{a^2(e^2-1)}{a^2(1+e)}\Rightarrow e=2$