Maximizing area Among all rectangles centered at the origin with vertices on the ellipse x2/a2 + y2/b2 = 1, what are the dimensions of the rectangle with the maximum area (in terms of a and b)? What is that area?

Solution 49REStep 1: In this problem we need to find the maximum area of the rectangle.Given : Ellipse is + = 1. Maximizing area among all rectangles centered at the origin with vertices on the Ellipse + = 1.Let , us consider (x , y) is a vertex of the rectangle.The related graph is shown below ;