A whispering chamber is a horizontal ellipse 100 feet long and 60 feet wide, centered at the origin. How far apart are its two foci?

1. The room is longer than it is wide, so the 100 feet run along the major axis. 2. The major axis has length 2a, so 2a is 100 feet and a is 50 feet. 3. The width of 60 feet is the minor axis, so 2b is 60 feet and b is 30 feet. 4. Then a squared is 2500 square feet and b squared is 900 square feet. 5. For an ellipse, c squared equals a squared minus b squared, giving 1600 square feet. 6. Taking the square root, c is 40 feet, the distance from the center to one focus. 7. The foci sit on opposite sides of the center, so they are 2c, or 80 feet, apart. 8. Answering 40 feet reports c alone and forgets the second focus. 9. Answering 60 feet just repeats the width of the room. 10. Answering 30 feet reports b, the half-width, which is not a focal distance. _Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.1 The Ellipse_