Identify the hyperbolas (represented by equations) whose centers are at (2, 1)

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.