When the transverse axis is horizontal, a hyperbola centered at (h,k) has formula (x-h)^2/a^2-(y-k)^2/b^2=1. Plug in h=2, k=1, the formula is (x-2)^2/a^2-(y-1)^2/b^2=1 for some a,b. If the transverse axis is vertical, the formula is (y-h)^2/a^2-(x-k)^2/b^2=1, and (y-2)^2/a^2-(x-1)^2/b^2=1 in our case.
