Question

Find the eccentricity of the ellipse if Length of latus rectum $=$ half of major axis.

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

Answer 1

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

Here given, $\frac{2b^2}{a}=\frac{1}{2}\cdot 2a\Rightarrow 2b^2=a^2$
$\therefore e=\sqrt{(1-\frac{b^2}{a^2})}=\sqrt{(1-\frac{1}{2})}=\frac{1}{\sqrt{2}}.$