I have to plot the hyperbola (3 of them actually) in MATLAB, and so it'd be good if I could find some sort of general formula.
The foci do not necessarily have to be on the axes (e.g. $(5,3)$ and $(4,8)$ can also be the foci). I have the difference in distances between them at a point which lies on the hyperbola. Will there be a general equation describing this hyperbola? If yes, what will it be? (e.g. say the points are $(x_1,y_1)$ & $(x_2,y_2)$ and difference in distance is $d$).
I know that I can shift and rotate the axes so that I get what I want, but I wanted to know if there was a better method, since while plotting i'll have to reconvert the values into the normal axes.
I'm going to try trilateration, which is why i'm asking for the equation.