For $x^2$/$a^2$ - $y^2$/$b^2$ = 1, compute S1 = $x1^2$/$a^2$ - $y1^2$/$b^2$ - 1. S1 < 0: inside (between the two branches), S1 = 0: on the hyperbola, S1 > 0: outside (in the same region as a branch). Note: "inside" for a hyperbola means between the branches, while "outside" means on the side of a branch. The centre (0,0) gives S1 = -1 $\frac{inside}{between branches}$.