Question

An architect wishes to design a large room 122 feet long that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse whose foci are to be located 14 feet to the right and the left of center. Find the height h of the elliptical ceiling ( to the nearest tenth of a foot.)

Answer 1

in an ellipse with semi axes a and b, the foci are at distance c from the center, where

a^2 = b^2 + c^2

Here, a = 61 and c = 14
The height will be the semi-minor axis, b

61^2 = b^2 + 14^2
b^2 = 3525
b = 59.4