Intersection between line and hyperbola
I am currently working on a research project related to pathfinding, and it requires us to solve an essential geometry problem: finding the intersection between line and hyperbola (a hyperbola may not be vertical or horizontal to x or y-axis ). I saw Geogebra have this function, so I just wonder how you program it in detail. Does it guarantee to find the intersections in constant time? Also, is there any source code available? any explanation about the math behind it?
Any information would be a great help! thanks in advance.