Question

Find the area of greatest rectangle that can be inscribed in an ellipse

x²/a² + y²/b² = 1

Answer 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 = s (say)