An architect wishes to design a large room that will be a whispering gallery. The ceiling of the room has a cross section that is an ellipse with a major axis measuring 286 feet and a minor axis measuring 90 feet. Assume the center is at (0, 0)and the major axis lies on the x -axis. How far to the right and left of center are the foci located? Approximate the answer to the nearest tenth of a foot.
A)135.7 ft
B)271.5 ft
C)45.0 ft
D)143.0 ft
E)196.0 ft

Question

Quizplus · Accepted Answer

The distance of the foci from the center of an ellipse is given by the formula c = √(a² - b²), where a is the semi-major axis and b is the semi-minor axis. Here, a = 286/2 = 143 and b = 90/2 = 45. Calculating c gives √(143² - 45²) = √(20449 - 2025) = √18424 ≈ 135.7 ft.

An Architect Wishes to Design a Large Room That Will