The equation for a circle centered at the origin on a coordinate plane is
x^2 + y^2 = radius^2
so, we can tell from your original equation that the radius of the circle is 7, because 7^2 = 49.
Just like moving a parabola using the y=x^2 equation, if we change the circle equation to
(x-1)^2 + (y+2)^2 = 49
we move it 1 unit to the right, and two units down. So since the center started at (0,0) the new center will be (1,-2). Hope this helps!