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Q.
If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be $1 / 2$, then length of the minor axis is
Conic Sections
Solution:
Given that, $\frac{a}{e}-a e=8$
Also,$\Rightarrow a=\frac{8 e}{1-e^2}=\frac{8.4}{2(3)}=\frac{16}{3}$
$\therefore b=\frac{16}{3} \sqrt{\left(1-\frac{1}{4}\right)}=\frac{16}{3} \frac{\sqrt{3}}{2}=\frac{8 \sqrt{3}}{3}$
$e=\frac{1}{2}$
Hence, the length of minor axis is $\frac{16 \sqrt{3}}{3}$.