Question

An ellipse has OB as a semi-minor axis. F and F' are its foci and the angle FBF' is a right angle. Then, the eccentricity of the ellipse is ___

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

Answer 1

The correct option is A

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

Since, angle FBF' is right angled.
$\therefore$ (Slope of FB). (Slope of F'B) = -1

$\Rightarrow \left(\frac{0-b}{ae-0}\right).\left(\frac{0-b}{-ae-0}\right)=-1$.
$\Rightarrow \frac{b^2}{-a^2{e}^2}=-1\Rightarrow b^2=a^2{e}^2$
$\Rightarrow a^2(1-e^2)=a^2{e}^2$
$\Rightarrow e^2=\frac{1}{2}\Rightarrow e=\frac{1}{\sqrt{2}}$