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, the eccentricity of the ellipse is equals to:

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

Answer 1

The correct option is C $\frac{1}{2}$

$ThetriangleSTBisequilateral,$

$DistanceSB=ST=2ae$

$DistanceTB==ST=2ae$

We know,

$SB+BT=2a$

$2ae+2ae=2a$

$Or,e=\frac{1}{2}$

Option [C]