Question

How do you graph `x^2+y^2-2x+6y+6=0`?

Answer 1

It's a circle of radius 2 centered at the point `(x,y)=(1,-3)`

Explanation:

To see this, rearrange terms a bit and complete the square for both the `x` terms and the `y` terms:

`x^2-2x+y^2+6y=-6`

`\Rightarrow (x^2-2x+1)+(y^2+6y+9)=-6+1+9=4`

`\Rightarrow (x-1)^2+(y+3)^2=2^2`