Question

A circle is described with minor axis of the ellipse as diameter. if the foci lie on the circle then the eccentricity of the ellipse is

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{\sqrt{7}}$
• D. $\frac{1}{\sqrt{5}}$

Answer 1

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

Let circle be $x^2+y^2=r^2$

Then $(0,b)$ satisfies it

$f^2=r^2......\left(1\right)$

Then $(ae,o)$ satisfies it

$a^2{e}^2=r^2.......\left(2\right)$

$\left(1\right)$ &$\left(2\right)$

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

$e^2=1-e^2$

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

$B$ is correct