If n is equal to 2, then it describes an ellipse (if a = b, then it describes a circle).
If n is greater than 2, then this is a "superellipse" (if a = b, then this is a supercircle).
As n increases, the ellipse becomes more "rectangularish", and as n approaches ∞, the limit is a rectangle (or a square if a=b).
What value must n have such that the figure has an area exactly halfway between the associated ellipse (when n=2) and rectangle (when n=∞)?
The graphs below, calculated by varying n with a = b = 1, show this property. Note that as n approaches zero, the curve degenerates into two crossed lines along the x- and y-axes.
