The LORAN (LOng RAnge Navigation) radio navigation system was widely used until the 1990s when it was superseded by the GPS system. In the LORAN system, two radio stations located at A and B transmit simultaneous signals to a ship or an aircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference | PA | 2 | PB |, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure). Suppose that station B is located 400 mi due east of station A on a coastline. A ship received the signal from B 1200 microseconds (ms) before it received the signal from A. (a) Assuming that radio signals travel at a speed of 980 ftyms, find an equation of the hyperbola on which the ship lies. (b) If the ship is due north of B, how far off the coastline is the ship?
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