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Let the distance between a focus and the...

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 `(sqrt(3)k)/2` is ____________

Text Solution

Verified by Experts

`(a)/(e)-ae=8`
or `2a-(a)/(2)=8`
or `a=(16)/(3)`
`b^(2)=a^(2)(1-e^(2))=(256)/(9)(1-(1)/(4))=(64)/(3)`
`:.` Length of minor axis `=2b=(16)/(sqrt(3))`
`:. k=8`
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