Rotation of Axis and Hyperbolic Sound Travelling Word problem?

[amd123]

Homework Statement

6x^2-6xy+14y^2-45=0

Two recording devices are set 2400 feet apart, with the device at Point A to the west of the device at point B. At a point on a line between the devices, 400 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation?

Homework Equations

I know the standard form of a hyperbola and I know that you have to use cot 2X = 4/3.
I don't know where to go from there.

The Attempt at a Solution

I've attempted the problem multiple times but I don't have my digi cam to take pictures of it.

 

[fzero]

Can you find an expression for the time difference in terms of the distance between the point of an explosion and points A and B? (You can leave the speed of sound in as an unknown, it cancels out in the end.) For the 2nd case, the distances are two sides of a right triangle, so the Pythagorean formula gives you another relationship between them.

 

[HallsofIvy]

You give an equation of a hyperbola, then a word problem that says nothing at all about the equation. What is the relationship between the problem and the equation? Also you say that "cot(2X)= 4/3" without any indication of what X is or what relationship it has with the problem.