Question

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is $90^{\circ}$ The eccentricity of the ellipse is

• A. $\frac{1}{8}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\sqrt{\frac{2}{3}}$
• D. $\sqrt{\frac{1}{2}}$

Answer 1

Answer: (D)

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

Answer 2

In $\Delta OSA$, $tan\, \frac{\pi}{4}=\frac{ae}{b}$
$\Rightarrow 1=\frac{ae}{b}$
$\Rightarrow e^{2}=\frac{b^{2}}{a^{2}}$
$\because e^{2}=1-\frac{b^{2}}{a^{2}}$
$\Rightarrow e^{2}=1-e^{2}$
$e^{2}=\frac{1}{2}$
$\Rightarrow e=\sqrt{\frac{1}{2}}$