Question

$S$ and $T$ are the foci of an ellipse and $B$ is an end of the minor axis. If $STB$ is an equilateral triangle, then what is the value of $e$ ?

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (C)

$\frac{1}{2}$

Distance between foci $=2ae$
Distance between foci and end of minor axis is $\sqrt{b^2+a^2{e}^2}$
$\therefore 2ae=\sqrt{b^2+a^2{e}^2}$
$4a^2{e}^2=b^2+a^2{e}^2$
$3a^2{e}^2=b^2=a^2(1-e^2)$
$4e^2=1$
$e=\frac{1}{2}$