Question

An ellipse has OB as 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. $\frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{2}{3}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

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

Answer 2

Since $\angle FBF' = \frac{\pi}{2}$

∴ $\angle FBC = \angle F'BC = \frac{\pi}{4}$

∴ $CB = CF \Rightarrow b = ae$

⇒ $b^{2} = a^{2}e^{2}$ ⇒ $a^{2}(1 - e^{2}) = a^{2}e^{2}$

⇒ $1 - e^{2} = e^{2}$⇒ $2e^{2} = 1$⇒ $e = \frac{1}{\sqrt{2}}$