NIMCET 2016 Question Paper with solutions

The vertices of any rectangle inscribed in an ellipse is given by (±a cos θ, ± b sin θ)
The area of the rectangle is given by A(θ) = 4ab cos θ sin θ
= 2ab sin 2θ
So. the area is maximum when sin(2θ) = 1
Hence, the maximum area is when $2\mathit{\theta }=\frac{\mathit{\pi }}{2}$
i.e, $\mathit{\theta }==\frac{\mathit{\pi }}{4}$ the maximum area is A = 2ab