Whispering Gallery  An architect wishes to design a large room 100 feet long that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse, as shown in the following figure.

  

      

  

If the foci are to be located 32 feet to the right and the left of center, find the height h of the elliptical ceiling (to the nearest tenth of a foot).
 

Elliptical ceiling of a whispering gallery h -50 | y 100 ft Foci 32 ft 50 X