Question

If a pebble is dropped into a pond in the shape of an ellipse at the location of one focus, the waves will converge at the location of the other focus. If the pond has a major axis of 40 feet and a minor axis of 24 feet, how far apart are the foci?

Answer 1

The two foci are 64 feet apart. For an ellipse centered at (0,0), the formula for the distance from one focus to the origin is \sqrt(a^2-b^2), where a is the length of the major axis and b is the length of minor axis. In this case, \sqrt(40^2-24^2)=32. Since the two foci are symmetric about the origin, their distance in between is 2*32=64.