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Question

If the ellipse x2a27+y2135a=1 is inscribed in a square of side length 2a, then a is equal to

A
65
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B
(,7)(7,13/5)
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C
(,7)(13/5,7)
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D
no such a exists
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Solution

The correct option is D no such a exists
Since sides of the square are tangent and perpendicular to each other, so the vertices lie on director circle.
x2+y2=(a27)+(135a)
=a2(2), a is side of the square
(a27)+(135a)=a2
a=65
But for an ellipse to exist a27>0 and 13 - 5a>0
aϵ(,7)
Hence, a65
Hence, no such a exists.

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