Chapter 10.1, Problem 97E

Lamé curves The Lamé curve described by ${\left|\frac{x}{a}\right|}^n+{\left|\frac{y}{b}\right|}^n=1$, where a, b, and n are positive real numbers, is a generalization of an ellipse.

1. a. Express this equation in parametric form (four pairs of equations are needed).
2. b. Graph the curve for a = 4 and b = 2, for various values of n.
3. c. Describe how the curves change as n increases.