Calculating Distance and Equation for a Hyperbola Using LORAN Stations

[uselessjack]

Homework Statement

( URL of image in case it doesn't display : http://imgur.com/wrzYH.png )

The axes x and y are measured in miles.

In the figure, the LORAN stations at A and B are 520 mi apart, and the ship at P receives station A's signal 2,640 microseconds (ms) before it receives the signal from B.

A) Assuming that radio signals travel at 960 ft/ms, find | d(P, A) - d(P, B)|

B) Find an equation for the branch of the hyperbola indicated in red in the figure, using miles as the unit of distance.

C) If A is due north of B, and if P is due east of A, how far is P from A?
My attempt at a solution
The only thing I was able to somewhat figure out was Part A, but I'm not sure if my logic was correct. I multiplied 960 by 2640 to get 2,534,400 and put that was my answer.

 

[LCKurtz]

I would start by calling A = (0,a) and B = (0,-a) and P = (x,y). Then remember that a hyperbola is the locus of a point moving such that the differences of its distances from two points is a constant d. The two points are the foci. First figure out the equation with those variables. Put the numbers in last.