Question

The latus rectum subtends a right angle at the centre of the ellipse then its eccentricity is

• A. $2\sin {18}^o$
• B. $2\cos {18}^o$
• C. $2\sin {54}^o$
• D. $2\cos {54}^o$

Answer 1

The correct option is A $2\sin {18}^o$

If latus rectum subtends right angle at centre then

$\tan {45}^{\circ }=\frac{\frac{b^2}{a}}{ae}$

$e=\frac{b^2}{a^2}=1-e^2$

$e^2+e-1=0$

$\Rightarrow e=\frac{-1+\sqrt{5}}{2}=2\sin {18}^{\circ }$