Question

If the minor axis of an ellipse subtends an angle ${60}^o$ at each focus, then $e=$

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{2}{\sqrt{3}}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is A $\frac{\sqrt{3}}{2}$

$e=\sin \theta$ where $\theta$ is the angle subtended by minor axis at focus

$\Rightarrow e=\sin {60}^{\circ }$

$\therefore e=\frac{\sqrt{3}}{2}$