I need to draw a paramaterised crescent using graphics primitives. I’ve looked at the answers to this question but I’m hoping my problem with tighter constraints is solvable.
There are 2 intersecting ellipses with their centres on the X axis:

with the constraints:
- A, B, C, D and L are known
- The elllipses do intersect: A/2 + C/2 > L
- The axes A and C are on the X axis
- The axes B and D are parallel to the Y axis
Is there a direct, non-iterative solution to find X,Y?
I realise this is more Math than programming, but I’m looking for code (C, C#, VB, …) not algebra, and I feel there’s a wider audience here.
Thanks!
Looks like it indeed cannot be done