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 (0,5√3), 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 C5 Let equation of ellipse x2a2+y2b2=1 2a−2b=10 ...(1) ae=5√3 ...(2) 2b2a=? b2=a2(1−e2) b2=a2−a2e2 b2=a2−25×3 ⇒b=5 and a=10 ∴ length of L.R=2(25)10=5