The LORAN (LOng RAnge Navigation) radio navigation system was widely used until the 1990s when it was superseded bythe GPS system. In the LORAN system, two radio stations located at A and B transmit simultaneous signals to a ship or anaircraft located at P. The onboard computer converts the time difference in receiving these signals into a distance difference|PA| = |PB|, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola(see the figure).coastline430 mitransmitting stationsPBSuppose that station B is located 430 mi due east of station A on a coastline. A ship received the signal from B1,200 microseconds (us) before it received the signal from A.(a) Assuming that radio signals travel at a speed of 980 ft/µs, find an equation of the hyperbola on which the ship lies.(Use x as the axis along the coastline, and center your coordinate system between A and B. Values should be inmiles.)(b) If the ship is due north of B, how far off the coastline (in mi) is the ship? (Round your answer to the nearest mile.)mi

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The LORAN (LOng RAnge Navigation) radio navigation system was widely used until the 1990s when it was superseded by the GPS system.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|- |PB|, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure).

The LORAN (LOng RAnge Navigation) radio navigation system was widely used until the 1990s when it was superseded by the GPS system.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|- |PB|, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola (see the figure).

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The LORAN (LOng RAnge Navigation) radio navigation system was widely used until the 1990s when it was superseded by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| = |PB|, and this, according to the definition of a hyperbola, locates the ship or aircraft on one branch of a hyperbola
(see the figure).
coastline
430 mi
transmitting stations
P
B
Suppose that station B is located 430 mi due east of station A on a coastline. A ship received the signal from B
1,200 microseconds (us) before it received the signal from A.
(a) Assuming that radio signals travel at a speed of 980 ft/µs, find an equation of the hyperbola on which the ship lies.
(Use x as the axis along the coastline, and center your coordinate system between A and B. Values should be in
miles.)
(b) If the ship is due north of B, how far off the coastline (in mi) is the ship? (Round your answer to the nearest mile.)
mi

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