answer the question below

Question

A greenhouse is shaped like a semi-ellipsoid. If the greenhouse is 40 feet long and has a maximum height of 15 feet, how far from the center of the greenhouse should a person stand so that he is on a focus of the ellipsoid?

Answer 1

40 = 2a

a =20

15 = 2b

b =7.5

foci are (c,0) and (-c,0)

c^2 = a^2 -b^2 = 400-56.25 = 343.75

c = sqr343.75 = 18.54049622 = about 18.5

c= about 18.5 feet from the center