Question

Statuary Hall is an elliptical room in the United States Capitol Building in Washington, D.C. The room is also referred to as the Whispering Gallery because a person standing at one focus of the room can hear even a whisper spoken by a person standing at the other focus. A student takes measurements of the room and estimates that the dimensions of Statuary Hall are 47 feet wide by 94 feet long.

(a) Find an equation for the shape of the floor surface of the hall. (Assume the major axis is horizontal and the center of the room is at the origin.)

(b) Determine the distance between the foci. (Round your answer to one decimal place.)

Answer 1

a = 94/2 = 47
b = 47/2 = 23.5

x^2/47^2 + y^2/23.5^2 = 1
now google ellipse to find focus :)

Answer 2

for the focus, c^2=a^2-b^2
The distance between the foci is 2c

Answer 3

"the dimensions of Statuary Hall are 47 feet wide by 94 feet long." That's actually wrong. Instead, "Statuary Hall is 92 ft. wide and 97 ft. long." The hall is only half an ellipse as a set of columns cuts off the other (non-existing) half of the ellipse. Look at floor plans and you can see that the hall is almost circular.