Chapter 4.3, Problem 89E

Area of an Ellipse Consider the ellipse

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a+b=20$

(a) The area of the ellipse is given by $A=\pi ab$. Write the area of the ellipse as a function of

$a$.

(b) Find the equation of an ellipse with an area of 264 square centimeters.

(c) Complete the table using your equation from part (a), and make a conjecture about the

shape of the ellipse with maximum area.

(d) Use a graphing utility to graph the area function and use the graph to support your

conjecture in part (c).