Ellipse Question 4
Question 4 - 2024 (30 Jan Shift 1)
If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :
(1) $\frac{\sqrt{5}}{3}$
(2) $\frac{\sqrt{3}}{2}$
(3) $\frac{1}{\sqrt{3}}$
(4) $\frac{2}{\sqrt{5}}$
Show Answer
Answer (4)
Solution
$2 b=ae$
$\frac{b}{a}=\frac{e}{2}$
$e=\sqrt{1-\frac{e^{2}}{4}}$
$e=\frac{2}{\sqrt{5}}$
