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**