Question

If $S$ and $S^{{}^{\prime }}$ are the foci and $B$ is an endpoint of the minor axis of an ellipse. If $\angle SB{S}^{{}^{\prime }}={120}^o$ then its eccentricity is:

• A. $\frac{\sqrt{5}}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

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

$\angle SB{S}^1={120}^{\circ }$
$\tan {30}^{\circ }=\frac{b}{ae}=\frac{1}{\sqrt{3}}$
$\sqrt{3}b=ae$
$\sqrt{3}a\sqrt{1-e^2}=ae$
$3-3e^2=e^2$
$e=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}$