The base of an auditorium is in the form of an ellipse 200 ft. long and 100 ft. wide. A pin dropped near one focus can clearly be heard at the other focus. Determine the distance between the foci to the nearest tenth of a foot. Show each step of the solution.

ANSWER:

The foci are 173.2 ft. apart.

The ellipse of the auditorium has a major axis of 200 ft. and a minor axis of 100 ft., which I determined from the ellipse’s given length and width.

Major axis = 2a = 200
Minor axis = 2b = 100

Therefore, a = 100 and b = 50.

Use the formula c^2 = a^2 - b^2 to find the distance from the center to the focus.

c^2 = 100^2 - 50^2
c^2 = 7500
√c^2 = √7500
c = 86.6

The distance between the two foci will be equal to twice the value of c.

2(86.6) = 173.2

The foci are 173.2 ft. apart.