Q.

Let the distance between a focus and the corresponding directrix of an ellipse be 8 and the eccentricity be 1/2.If the length of the minor axis is k, then 3k/2 is __________.

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answer is 8.

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Detailed Solution

ae−ae=8 or 2a−a2=8 or a=163b2=a21−e2=25691−14=643∴Length of minor axis =2b=163∴k = 8
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Let the distance between a focus and the corresponding directrix of an ellipse be 8 and the eccentricity be 1/2.If the length of the minor axis is k, then 3k/2 is __________.