I need a plotter for a system of hyperbolic equations

[barryj]

I am trying to illustrate how hyperbolic navigation works. In the process, I need a program that will plot two hyperbolic equations and solve their intersection. I would rather not have to change the equation into function form if possible. I know that the plots will be two hyperbolas that are rotated from the normal x-y axis.

 

[Mark44]

I am trying to illustrate how hyperbolic navigation works. In the process, I need a program that will plot two hyperbolic equations and solve their intersection. I would rather not have to change the equation into function form if possible. I know that the plots will be two hyperbolas that are rotated from the normal x-y axis.

I think you might be asking about LORAN. Here's a link to some of the mathematics behind this technology -- http://mathcentral.uregina.ca/beyond/articles/LoranGPS/Loran.html

 

[barryj]

LORAN is the best example of hyperbolic navigation. However, some cities, I have been told, set up microphones around the city to detect gun shots. The difference in time of arrival of the shot sound can be used to figure out where the shot originated from. I have attached my example.

Knowing the position of three sources, and the difference in path lengths, find x,y.