factor: x^2+y^2+ax+2y+4=0
First plug in the point (2,2) into the equation to find "a".
2^2+2^2+a(2)+2(2)+4=0
2a=-16
a=-8
So now with the value of a we have:
x^2+y^2-8x+2y+4=0
Let rearrange the terms:
x^2-8x+y^2+2y+4=0
Move the constant over to the right side of the equation.
x^2-8x+y^2+2y=-4
Completing the square is tricky but what needs to be done.
x^2-8x+16+y^2+2y+1=13
And then factor the sum and differences of squares.
(x-4)^2+(y+1)^2=13
Divide by 13.
(x-4)^2/13+(y+1)^2/13=0
Now it is in factored form, so we can get the center of the circle.
The center will be at (4,-1).