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Question

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is

A
23
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B
3
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C
32
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D
32
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Solution

The correct option is D 32
Let the equation of ellipse be x2a2+y2b2=1 (a>b)
Now, 2ae=6 and 2ae=12
ae=3 and ae=6
a2=18

a2e2=c2=a2b2=9b2=9
Length of latus rectum =2b2a=2×918=32

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