How to pythonically have partially-mutually exclusive optional arguments?

Question

As a simple example, take a class Ellipse that can return its properties such as area A, circumference C, major/minor axis a/b

Answer 1

For the bonus question it's probably sensible (depending on your use case) to calculate on request but remember the computed value if it's been computed before. E.g.

@property
def a(self):
    return self._calc_a()

def _calc_a(self):
    if self.a is None:
        self.a = ...?
    return self.a