Question

The latusrectum LL’ subtends a right angle at the centre of the ellipse, then its eccentricity is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

From the right angled triangle OSL,
$\tan {45}^{\circ }=\frac{SL}{OS}\Rightarrow \frac{b^2}{a}=ae$
$\Rightarrow a^2(1-e^2)=a^{2}e\Rightarrow e^2+e-1=0$
$\Rightarrow e=\frac{-1\pm \sqrt{1+4}}{2}\Rightarrow e=\frac{\sqrt{5}-1}{2}$