Let ABCD be rectangle having area A inscribed in an ellipse
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) ...(i)
Let the coordinate of A be (α,β)
∴ Coordinate of B = (α,-β), C = (-α,-β), D = (-α,β)
Now,
A = Length x Breadth
= 2α x 2β
A = 4αβ
For maximum or minimum value