Find the area of greatest rectangle that can be inscribed in an ellipse
x2/a2 + y2/b2 = 1
Let ABCD be the rectangle of maximum area with sides AB = 2x and BC = 2y, where C (x, y) is a point on the ellipse x2/a2 + y2/b2 = 1 as shown in the Fig.6.3
The area A of the rectangle is 4xy i.e. A = 4xy which gives A2 = 16x2y2 = * (say)
