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Question

The eccentricity of an ellipse x2a2+y2b2=1, whose latus rectum is half of its major axis, is .

A
e=12
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B
e=12
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C
e=122
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D
e=14
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Solution

The correct option is A e=12
Let a>b. Then, the latus rectum of the ellipse is 2b2a and the semimajor axis is a.
Given, 2b2a=aor 2b2=a2
Also for the ellipse,
b2 = a2(1e2)b2 = 2b2(1e2)On solving, e = 12

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