Question

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

Answer 1

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