If the foci are twenty-five feet from the center, then c = 25. You are given that the room will be 100 feet long, so the ends (the vertices) are clearly fifty feet from the center, so a = 50.

Usethe formularelating a, b, and c, to find the value of b. Then write the equation, centering the ellipse (for convenience) at the origin, so (h, k) = (0, 0).