The equation (x/a)2 + (y/b)2 = 1 is the standard form of an ellipse. What shape will the equations (x/a)3 + (y/b)3 = 1, (x/a)4 + (y/b)4 = 1, or generally (x/a)n + (y/b)n = 1 create? These equations are called Lamé curves, or superellipses, when n > 2. Investigate several Lamé curve graphs in a friendly graphing window. Assume that a > 0 and b > 0. You already know what effect the values of a and b have on an ellipse. Do they have the same effect on a Lamé curve? For fixed values of a and b, try different n-values, including positive, negative, whole-number, and rational values. Explore the graph shapes and properties for different values of n. Summarize your discoveries.