Question

If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be $\frac{1}{2}$ , then length of the minor axis is

• A. 3
• B. $4\sqrt{2}$
• C. 6
• D. None of these

Answer 1

The correct option is D

None of these

$\frac{a}{e}-ae=8$ . Also e = $\frac{1}{2}\Rightarrow a=\frac{8e}{(1-e^2)}=\frac{8.4}{2\left(3\right)}=\frac{16}{3}$

$\therefore$ b = $\frac{16}{3}\sqrt{(1-\frac{1}{4})}=\frac{16}{2}\frac{\sqrt{3}}{2}=\frac{8\sqrt{3}}{3}$

Hence the length of minor axis is $\frac{16}{\sqrt{3}}$ .