what is the center and randius of the circle

Question

x^2+y^2-12x+2y+33=0

Answer 1

(x-h)^2+(y-k)^2=r^2, where (h,k) is the center and r is the radius

x^2+y^2-12x+2y+33=0

rearrange terms

x^2-12x    +y^2+2y     =-33

complete the square for x and for y

12/2=6 and 6^2=36

2/2=1 and 1^2=1

add 36 and 1 to both sides

x^2-12x+36+y^2+2y+1=-33+36+1

(x-6)^2+(y+1)^2=2^2

(6,-1) is the center and 2 is the radius