Or perhaps just "Elliptical arc" if it's not half across the minor or major axis.
> What would i do in the case of the half ellipse where both endpoints of the
> open half have "parallel tan's", so no converging point to choose?
Usually for a NURBS representation of a circle or ellipse it will be made up of 90 degree arc pieces that are glued together.
If you want to make one made up of glued together arcs, use Join to join them into a segmented curve and then run Merge on it and it will fuse the 2 pieces into one segment with a "corner point" (fully multiple knot) between the pieces.
A good book that shows some other possible formulations is Curves and Surfaces For Computer Aided Geometric Design by Gerald Farin: https://archive.org/details/curvessurfacesfo0000fari_x6i3
Check out chapter 13 and 14 there.
There may be an example there with using a zero weight value for a non-converging control polygon but most CAD systems will not like to work with negative or zero weight values.
> The other brain pick was for fun to see if you had anything for me. I was looking
> into ways to find the foci of the ellipse...
Sounds like something Brian (Bemfarmer) would know. He hasn't been around in a while.
ellipse with foci.3dm