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Question

If the ellipse x2a23+y2a+4=1 is inscribed in a square of side length a2 then a is

A
4
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B
2
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C
1
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D
None of these
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Solution

The correct option is D None of these
Sides of the square will be perpendicular tangents to the ellipse so, vertices of the square will lie on director circle. So diameter of director circle is
2(a23)+(a+4)=2a2+2a22a2+a+1=2aa=1But for ellipse a2>3&a>4
So there is no value of a which satisfy both.

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