An ellipse is the path of a point whose distances to two fixed foci have a constant sum.
The parametrization x=a cos t, y=b sin t lies on the ellipse. For foci (±c,0), where c²=a²−b² and a≥b>0, the two distances sum to 2a. As b approaches a, the foci merge and the ellipse becomes a circle.
The parameter t is not generally the polar angle of the point.