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Question

If the length of the minor axis of an ellipse is equal to the distance between their foci, then eccentricity of the ellipse is:

A
32
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B
32
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C
12
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D
2
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Solution

The correct option is C 12
Length of minor axis of an ellipse =2b
Distance between foci =2ae
According to the question,
2ae=2b
ae=b
a2e2=b2
We know, b2=a2(1e2)
a2e2=a2(1e2)
a2e2=a2a2e2
2a2e2=a2
2e2=1
e2=12
e=12


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