Solution
= Solution
Complete the squares in the two coordinates:
$$
(x-2)^2-4+4(y-1)^2-4=-4,
\qquad\frac{(x-2)^2}{4}+(y-1)^2=1.
$$
This standard equation of an <ellipse> is symmetric about $x=2$ and $y=1$. Its centre is therefore
$$
\boxed{(2,1).}
$$