The general equation for this circle is:

$\left(\frac{\textit{x}-3}{2}\right)^2-\left(\frac{\textit{y}-6}{2}\right)^2=1$

$\left(\frac{x-3}{2}\right)^2=\cos^2(t)$

$\left(\frac{y-6}{2}\right)^2=\sin^2(t)$