JEE MAIN - Mathematics (2024 - 30th January Morning Shift - No. 11)

If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :

$$\frac{1}{\sqrt{3}}$$

$$\frac{2}{\sqrt{5}}$$

$$\frac{\sqrt{3}}{2}$$

$$\frac{\sqrt{5}}{3}$$

$$\begin{aligned} & 2 b=a e \\ & \frac{b}{a}=\frac{e}{2} \\ & e=\sqrt{1-\frac{e^2}{4}} \\ & e=\frac{2}{\sqrt{5}} \end{aligned}$$