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

Jan 26, 2016

Draw a circle with center $\left(3 , - 1\right)$ and radius $4$.

#### Explanation:

${x}^{2} + {y}^{2} - 6 x + 2 y - 6 = 0$

$\rightarrow \textcolor{red}{{x}^{2} - 6 x} + \textcolor{b l u e}{{y}^{2} + 2 y} = \textcolor{g r e e n}{6}$

$\rightarrow \textcolor{red}{{x}^{2} - 6 x + 9} + \textcolor{b l u e}{{y}^{2} + 2 y + 1} = \textcolor{g r e e n}{6} \textcolor{red}{+ 9} \textcolor{b l u e}{+ 1}$

$\rightarrow \textcolor{red}{{\left(x - 3\right)}^{2}} + \textcolor{b l u e}{{\left(y + 1\right)}^{2}} = \textcolor{\mathmr{and} a n \ge}{{4}^{2}}$

which is the standard form for a circle with center $\left(3 , - 1\right)$ and radius $4$.

graph{x^2-6x+y^2+2y-6=0 [-8.1, 9.68, -5.404, 3.48]}