College algebra
posted by Missy .
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.)

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 semiminor axis, b
61^2 = b^2 + 14^2
b^2 = 3525
b = 59.4