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Question

Write the eccentricity of an ellipse whose latus-rectum is one half of the minor axis.

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Solution

Let the equation of ellipse are
x2a2+y2b2=1, where a>b
According to equation
2b2a=12×(2b)
2b2=ab
b2b=a2
b=a2
b2=a24
Now,
b2=a2(1e2)
a24=a2(1e2)
14=1e2
e2=114
e2=34
e=32

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