An ellipsoid is a 3D shape whose cross sections are ellipses. A lithotripter is a device in the shape of a half-ellipsoid that is used to crush kidney stones with shockwaves. An emitter is placed at the focus closer to the lithotripter and the kidney stone is placed at the other focus. A cross section of the lithotripter can be modeled by the ellipse shown below, centered at the origin with a horizontal major axis. If the emitter is placed 22.5 cm from a vertex of ellipse, and the stone is placed 61.6 cm from the emitter, write the equation of the ellipse