If the circle x2 - 4x + y2 + 2y = 4 is translated 3 units to the right and 1 unit down, what is the center of the circle?

The equation of a circle with center at (a, b) and radius r is: (x-a) ^2 + (y-b) ^2=r^2.

This circle has been translated from (0,0) to (a, b).

The equation of the circle in our case can be rewritten as: (x-2) ^2 + (y-2) ^2=2^2

Moving the graph 3 units to the right is: (x-2-3) ^2 + (y-2) ^2=2^2.

Moving the graph 1 unit down is: (x-2-3) ^2 + (y-2-1) ^2=2^2.

This gives the equation: (x-5) ^2 + (y-3) ^2=2^2

So, the center of the circle is: (5,3)