Question

Write the eccentricity of an ellipse whose latus-rectum is one half of the minor axis.

Answer 1

\[\text{ According to the question, the latus rectum is half its minor axis }.\]
\[i . e . \frac{2 b^2}{a} = \frac{1}{2} \times 2b\]
\[ \Rightarrow 2b = a\]
\[\text{ Now }, e = \sqrt{1 - \frac{b^2}{a^2}}\]
\[ \Rightarrow e = \sqrt{1 - \frac{b^2}{4 b^2}}\]
\[ \Rightarrow e = \sqrt{1 - \frac{1}{4}}\]
\[ \Rightarrow e = \frac{\sqrt{3}}{2}\]