Question

--

Answer 1

You need to put it in the form:
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius.

x^2+y^2-2x+6y+9=0
Group the x term together and the y terms together:
x^2 - 2x + y^2 + 6y + 9 = 0
complete the squares (x^2 - 2x) and (y^2 + 6y) separately and then put them together.

Answer 2

x^2 - 2x + y^2 + 6y + 9 = 0
complete the square of x^2 - 2x.
Divide coefficient of x by 2: -2/2 = -1. This number will go inside the parenthesis that will be squared. Subtract square of (-1).
x^2 - 2x = (x - 1)^2 - (-1)^2 = (x-1)^2 - 1

complete the square of y^2 + 6y:
Divide coefficient of y by 2: 6/2 = 3. This number will go inside the parenthesis that will be squared. Subtract square of (3).
y^2 + 6y = (y+3)^2 - 3^2 = (y+3)^2 - 9

Put them together:
x^2 - 2x + y^2 + 6y + 9 = 0
(x-1)^2 - 1 + (y+3)^2 - 9 + 9 = 0
(x-1)^2 - 1 + (y+3)^2 = 0
(x-1)^2 + (y+3)^2 = +1
(x-1)^2 + (y+3)^2 = 1^2
compare this to:
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius.
center is (1, -3) and radius = 1

Answer 3

?