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

Jul 24, 2015

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

#### Explanation:

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

${x}^{2} - 2 x + {y}^{2} + 6 y = - 6$

$\setminus R i g h t a r r o w \left({x}^{2} - 2 x + 1\right) + \left({y}^{2} + 6 y + 9\right) = - 6 + 1 + 9 = 4$

$\setminus R i g h t a r r o w {\left(x - 1\right)}^{2} + {\left(y + 3\right)}^{2} = {2}^{2}$