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:

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answer is B.

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Detailed Solution

2ae=6 and 2ae=12⇒ae=3 and ae=6⇒a2=18⇒b2=a2−a2e2=18−9=9 ∴Length of latus rectum=2b2a=2×932=32