Question

If the length of the minor axis is half of the length of the major axis of an ellipse, then the value of $4e^2$, where $e$ is the eccentricity of the ellipse, is

Answer 1

Let $2a$ and $2b$ be the length of major axis and minor axis respectively.
According to the given conditions,
$2b=\frac{1}{2}\times 2a\Rightarrow \frac{b^2}{a^2}=\frac{1}{4}\Rightarrow e^2=1-\frac{b^2}{a^2}\Rightarrow e^2=\frac{3}{4}\therefore 4e^2=3$