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Question

The eccentricity of the ellipse x2a2+y2b2=1 if its latus rectum is equal to one half of its minor axis, is
(a) 12

(b) 32

(c) 12

(d) none of these

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Solution

(b) e=32According to the question, the latus rectum is half its minor axis.i.e. 2b2a=12×2b2b2=aba=2bNow, e=1-b2a2e=1-b24b2e=1-14e=32

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