Question

S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is

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

Answer 1

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

Given, $\frac{b}{ae}=\sqrt{3}\Rightarrow b=\sqrt{3}ae$
$e^2=\frac{a^2-3a^2{e}^2}{a^2}=1-3e^2$
$4e^2=1\Rightarrow e=\frac{1}{2}$