Question

A designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 40 meters, which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guests to stand to experience his whisper chamber will be 5 meters from the center of the warehouse space, which will act as the foci. How far out from the center, along the minor axis, should he build his whisper chamber?

19.4 m
38.7 m
39.7 m
79.4 m

Answer 1

Explanation:

We are given that the longest length of the warehouse space is 40 meters, which will be the major axis of the ellipse. We are also given that the foci of the ellipse will be located 5 meters from the center of the warehouse space.

Let us denote the length of the minor axis of the ellipse as 2b. We can use the formula for the distance between the foci of an ellipse to find the value of b:

c = 5 (distance between foci and center)

a = 20 (half of the major axis)

b = ?

c^2 = a^2 - b^2

Substituting the values, we get:

5^2 = 20^2 - b^2

Simplifying, we get:

b^2 = 20^2 - 5^2

b^2 = 375

b = √375

b ≈ 19.4 meters

Therefore, the answer is (A) 19.4 m. The designer should build his whisper chamber 19.4 meters out from the center, along the minor axis.