Question

Find the eccentricity of an ellipse whose latus rectum is  half of its major axis. 

Answer 1

\[\text{ According to the question, the latus rectum is half its minor axis }.\]
\[\text{ i . e } . \frac{2 b^2}{a} = \frac{1}{2} \times \left( 2a \right)\]
\[ \Rightarrow 2 b^2 = a^2 \]
\[ \Rightarrow a^2 = 2 b^2 \]
\[\text{ Now }, e = \sqrt{1 - \frac{b^2}{2 b^2}}\]
\[ \Rightarrow e = \sqrt{1 - \frac{1}{2}}\]
\[ \Rightarrow e = \frac{1}{\sqrt{2}}\]