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 :
JEE · Math · previous-year question
- A.$$\frac{1}{\sqrt{3}}$$
- B.$$\frac{2}{\sqrt{5}}$$correct
- C.$$\frac{\sqrt{3}}{2}$$
- D.$$\frac{\sqrt{5}}{3}$$
Answer
B. $$\frac{2}{\sqrt{5}}$$
Explanation
$$\begin{aligned} & 2 b=a e \\ & \frac{b}{a}=\frac{e}{2} \\ & e=\sqrt{1-\frac{e^2}{4}} \\ & e=\frac{2}{\sqrt{5}} \end{aligned}$$
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