I want to determine the largest area ellipse inscribed in a rectangle, in order to write a code that can determine the lengths c and d given a and b (see image here). I know the obvious answer would be c and d are halves of a and b, but I want the derivation (and also the maximum area) so I can stop thinking about this, saddly I can't seem to figure this one out. I remember doing the opposite in school (rectangle inside ellipse) but can't do it properly now.
Hope you can help me.