Hyperbolas are used in finding positions. A ship at sea can pick up signals form several radar beacons. Knowing the difference in the patterns in the signals received gives the difference in the distances to the beacons. So, a navigator can determine, using two of the beacons, a hyperbola . The ship's position is a point on that hyperbola. Using a third beacon, the navigator can determine a second hyperbola. Since the navigator knows roughly where he is , he can find out exactly where he is by finding the intersections of the hyperbolas. seismologists use a simiar method to determine earthquake positions.
Examples of these applications of hyperbolas can be found in the newer "MTV" Algebra II books.