Question

If the latus rectum subtends a right angle at the centre of the hyperbola then its eccentricity

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$Given,\angle SOL={45}^{\circ }$


$\therefore tan{45}^{\circ }=\frac{SL}{OS}\Rightarrow SL=OS\Rightarrow \frac{b^2}{a}=ae\Rightarrow a^2(e^2-1)=a^{2}e\Rightarrow e^2-e-1=0\Rightarrow e=\frac{\sqrt{5}+1}{2}$