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Question

In a ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at (0,53), then the length of its rectum is:

A
10
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B
8
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C
5
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D
6
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Solution

The correct option is C 5
Let equation of ellipse x2a2+y2b2=1
2a2b=10 ...(1)
ae=53 ...(2)
2b2a=?
b2=a2(1e2)
b2=a2a2e2
b2=a225×3
b=5 and a=10
length of L.R=2(25)10=5

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