Question

$S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis, if $△STB$ is equilateral, then $e$ is equals to:

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

Answer: (C)

$\frac{1}{2}$

$\tan {60}^0=\frac{OB}{OS}$

$\Rightarrow \sqrt{3}=-\frac{b}{ae}\Rightarrow \frac{b}{a}=e\sqrt{3}$

Now, $e^2=1-\frac{b^2}{a^2}\Rightarrow e^2=1-3e^2$

Now $4e^2=1\Rightarrow e=\frac{1}{2}$