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.
You know the value of the semi-axis major, a = 50. You also know a point on the ellipse: (40, 10) (You actually know the point (-40, 10) as well, since the ellipse is symmetrical.)
Plug all this into your equation:
This is an equation for your semi-axis minor, b, which tells you the height of the ellipse (bridge) above the origin (center of the bridge.)