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

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None of these

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Solution

The correct option is D
None of these

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

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

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

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