At what point does a circle start losing area when being flattened?

The area ratio decreases slowly at first then more rapidly.
The area of an ellipse is A=pi x a X b, a and b are the 1/2 major and 1/2 minor axis. If a = r = b the area is A=pi X r2, which is a circle. Not hard to graph this but you will have to write the area of the ellipse in terms of the circumference.