GATE 2015 EC – Question 39
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse $x^2 + 4y^2 = 1$ is ________.
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Correct answer: 0.95 to 1.05
Explanation
The ellipse has semi-axes $a = 1$ and $b = \frac{1}{2}$. A rectangle with vertices $(\pm a\cos\theta, \pm b\sin\theta)$ has area $4ab\sin\theta\cos\theta = 2ab\sin 2\theta$, whose maximum is $2ab = 1$.