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

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Answer 1 · 2015-07-24T16:22:55

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

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

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

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

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

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