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# square inscribed in an ellipse question

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A square is inscribed in the ellipse $$\frac{x^2}{3} + \frac{y^2}{6} = 1,$$ so that its sides are parallel to the coordinate axes. Find the area of the square.

Dec 5, 2018

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The corners of the square are

$$\left(\pm \dfrac s 2, \pm \dfrac s 2\right) so \\ \dfrac{s^2}{12}+\dfrac{s^2}{24}=1\\ 3s^2 = 24 \\ s^2 = 8 =\text{ area of the square}$$

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Dec 5, 2018