The best way to calculate our curves is to describe them with a few points. For lines and Bezier curves, the normal Svg path representation consists of the control points.
The situation is completely different with elliptical curves. In a normal Svg file you have a start and end point, but else you have
Radius in x-direction
Radius in y-direction
the angle of the ellipse axes against the coordinate axes
the information as to whether you want to display the larger or smaller part of the ellipse
information on whether the arc should move clockwise or counterclockwise
Here you first have to do some trigonometry to get the center and the two main axes. When having the center you can calculate quickly and easily again.