Two radio transmitters positioned 200200 mi apart along the shore send simultaneous signals to a ship that is 100100 mi offshore and sailing parallel to the shoreline. The signal from transmitter S reaches the ship 500500 microseconds later than the signal from transmitter T. The signals travel at a speed of 186,000 miles per second, or 0.186 mile per microsecond. Find the equation of the hyperbola with foci S and T on which the ship is located. (Hint: For any point on the hyperbola, the absolute value of the difference of its distances from the foci is 2a.)