Question

circle
x^2+y^2-6x+12y+33=0

1. transform equation to standard form
2. graph
3. label centers
4. mark radius of each

Answer 1

complete the square

x2 - 6x + ..... + y^2 + 12y + .... = -33
x^2 - 6x + 9 + y^2 + 12y + 36 = -33 + 9 + 36
(x+3)^2 + (y+6)^2 = 12

I am sure you can finish the question from here,
but...
I am puzzles by 3. and 4.
it says to label centres and in 4. to mark the radius of each.
That suggests that there are more than one circle.