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 50 yards, 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 10 yards 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 out his whisper chamber?
53.9 yd
45.8 yd
26.9 yd
22.9 yd

Answer 1

Answer:

22.9 yd

Step-by-step explanation:

The relation between the location of the focus (c), the vertex on the major axis (a) and the vertex on the minor axis (b) with respect the center is:

b² = a² - c²

From the question:

c: 10 yd

a: 50/2 = 25 yd

Replacing into the equation:

b² = 25² - 10²

b = √525

b = 22.9 yd