For the circle , the largest triangle that can be drawn inside it is the equilateral triangle with side , whose area is .

The ellipse is obtained from the circle by the linear transformation with matrix . (In non-technical language, you get the ellipse from the circle by leaving the x-coordinate unchanged and expanding or shrinking the y-coordinate by a factor b/a.) This transformation alters areas by a factor b/a. So the largest triangle that can be inscribed in the ellipse has area , or square units when a=3 and b=7.