I'm trying to formulate a problem related with the Long Range Navigation(LORAN) System, that uses Hyperbolas to determine the position of a reciever(a ship for example). The Loran uses 1 master station and 2 slaves(and calculates de equation of the Hyperbola betwin the master and each of the slave stations) and if the stations are aligned at a 90 degree angle it's not hard to determine the equation for the 2 hyperbolas.
With the distance from point P to stations A and C, and the distance from A to C I can get the first equation, and doing the same to stations A and C I can the second equation and solve for x and y.(C is the master)
(x/a)^2 - (y/b)^2=1 (for an horizontal hyperbola)
My problem is when these stations aren't perfectly aligned. I'm not getting how i can incorporate the rotation of the hyperbola.Is there a equation for the Hyperbola when the axis is rotated ( I know i have to have some x*y in the equation but i can't figure it out). I attached a pic with what I'm looking for.