Question

A circle is described with minor axis of the ellipse as diameter. If the foci lie on the circle, then the eccentricty of the ellipse is

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. $\frac{1}{\sqrt{5}}$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

Foci lie on circle with minor axis as diameter

$\Rightarrow ae=b$

$e^2=\frac{b^2}{a^2}=1-e^2$

$e=\frac{1}{\sqrt{2}}$