The area of an ellipse is equal to A = ab (see figure). For the ellipse below,

Question:

The area of an ellipse is equal to A = ab (see figure). For the ellipse below, a + b = 20.

(a) Show that
A = a(20 ˆ’ a).
(b) Complete the table.

(c) Find two values of a such that A = 300.
(d) Use a graphing utility to graph the area equation.
(e) Find the a-intercepts of the graph of the area equation.
What do these values represent?
(f) What is the maximum area? What values of a and b yield the maximum area?