A whispering gallery is designed using an elliptical ceiling. It operates on the principle that the sound projected from one focus of an ellipse reflects off the ceiling and back to the other focus. The United States Capital contains such an elliptical room. The room is 96 feet in length, 46 feet in width, and has a ceiling that is about 23 feet high.

a) Write an equation modeling the shape of the room. Assume that it is centered at the origin and the major axis is horizontal.

Question

A whispering gallery is designed using an elliptical ceiling. It operates on the principle that the sound projected from one focus of an ellipse reflects off the ceiling and back to the other focus. The United States Capital contains such an elliptical room. The room is 96 feet in length, 46 feet in width, and has a ceiling that is about 23 feet high.

a) Write an equation modeling the shape of the room. Assume that it is centered at the origin and the major axis is horizontal.