How to obtain x and y coordinates of a curve as function of angle along circumference?

I want to know the x and y coordinates at a certain angle (sys2.phi) from a curve which runs around [0,0]. For a circle with radius R this can be found easily with formula's. However, for curves of different shapes it starts getting complicated. As an example I'm trying to get the radius of an ellipse as function of the angle along circumference (0-2pi). I thus want to know the coordinates from the geometry, is there a simple function to do so?

Thank you for your answers.