MathFoundations29: Parametrizing circles

[MemeMachine1]

Is there a natural way to parametrize hyperbolas, and all conics? All algebraic curves? All algebraic varieties of any dimension?

[njwildberger]

@MemeMachine1 This is a natural and important question. Any conic that has at least one point on it can be parametrized. Some cubics can be parametrized rationally, others not, and then is a crucial distinction between types of cubics. For higher degree curves or varieties the situation is even more complicated, and I suppose it is in general hard to tell if a given curve can be parametrized rationally.