Ellipse in a square

Geometry Level 4

If area of the ellipse x 2 16 + y 2 b 2 = 1 \frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1 inscribed in a square of side length 5 2 5\sqrt{2} is A, then A π \frac{A} {\pi} equals to:


The answer is 12.

Sanchit Ahuja by Sanchit Ahuja , 22, India

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2 solutions

Basically sides of the square form perpendicular tangents to the ellipse. There meeting point is the director circle. Using this we can find b=3. Now, area of ellipse =πab=12π=A Therefore, A/π=12

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Zerocool 141
Jan 21, 2017

now since it is inscribed in a square .it is obvious that there will be only on such square possible .whose vertices lie on director circle . also R=5 of that circle (by simple geometry ) . R^{2}=a^{2} + b^{2} b=3 area A =piab A/pi=12

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