Right that will be a solid ellipse with boundary |z-a|+|z-b|=M
Assuming you have two points in an Euclidian plane, with a distance D between the two.
If you would take the union of all possible curves connecting the two points, with a length smaller or equal to M, with M > D, what kind of shape would that give (and with what parameters) ?
Intuitively I would think it to be an ellipse.
(I'm sorry if this post is in the wrong sub-forum)