If OB is the semi - minor axis of an ellipse ,$\;F_{1}\;$ and $\;F_{2}\;$ are its foci and the angle between $\;F_{1}B\;$ and $\;F_{2}B\;$ is a right angle , then the square of the eccentricity of the ellipse is :

Question

$(a)\;\large\frac{1}{2} \qquad(b)\;\large\frac{1}{\sqrt{2}}\qquad(c)\;\large\frac{1}{2 \sqrt{2}}\qquad(d)\;\large\frac{1}{4}$