Originally Posted by

**HallsofIvy** If it is possible that the axes of the hyperbola are tilted with respect to the x and y axes the problem becomes much more complicated. However, **any** conic section (hyperbola, parabola, ellipse, circle and some special cases) can be written in the form $\displaystyle Ax^2+ Bxy+ Cy^2+ Dx+ Ey+ F= 0$. That has 6 parameters but we could always divide the entire equation by one of the so there are 5 independent parameters. That means that 5 points are sufficient to determine any conic section.