Question

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

Answer 1

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