I've been trying to find a way into solving this problem for about an hour, but nothing's clicking. The only information given is its length along the major axis and a point on the ellipse.
Here it is:
A bridge is to be built in the shape of a semielliptical arch and is to have a span of 100 feet. The height of the arch, at a distance of 40 feet from the center, is to be 10 feet. Find the height of the arch at its center.
So I know that A squared is 2500, but I can't figure out how to use the point (40,10) to arrive at the focus, which would then let me figure out the height.