Question

Statuary Hal is an elliptical room in the U.S. Capitol. Teh room is also called 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. Statuary Hall is 46 ft. wide and 97 ft. long.
a) Find an equation that models the shape of the room.
b) How far apart are the two foci?
c) What is the area of the floor of the room?

Just verifying if what I have done so far is correct...

a) 2a = 97
a = 48.5

2b = 46
b = 23

x^2/(48.5^2) + y^2/(23^2) = 1

b) c^2 = a^2 - b^2
c^2 = 48.5^2 - 23^2
c = 42.7

42.7 * 2 = 85.4 feet apart.

Please correct me if I am doing anything wrong.

Answer 1

I agree with all your answers, except you forgot to find the area
c) area = πab = π(48.5)(23) = 1115.5π or appr3504.4 square feet

Answer 2

"Statuary Hall is 46 ft. wide and 97 ft. 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.