The vertical cross section of a dome is semielliptical in sh

The vertical cross section of a dome is semi-elliptical in shape. The cross section is 270 feet long with a maximum height of 90 feet. Where should two people stand in order to maximize the whispering effect? The people should stand on opposite sides of the room each being located at one of the foci located feet from the wall. (Round to the nearest foot as needed.)

Solution

length of semi major axis a=270/2=135

length of semi major axis b=90

e =[1-(b/a)²]

e =[1-(90/135)²]

e =[1-(4/9)]

e =[5/9]

distance from the wall =a(1-e)

distance from the wall =135(1-[5/9])

distance from the wall =34 feet

people should stand on opposite sides of the room each being located at one of the foci located 34 feet from the wall