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

Feb 10, 2016

circle: centre (-1 , -3 ) , radius = 2

#### Explanation:

by rewriting the equation as ${x}^{2} + {y}^{2} + 2 x + 6 y + 6 = 0$

and comparing it to the general equation of a circle:

${x}^{2} + {y}^{2} + 2 g x + 2 f y + c = 0$

by comparison : 2g = 2 →g = 1 , 2f = 6 → f = 3 and c =6

now centre = (-g , -f ) = (-1 , -3 )

and radius $= \sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{1}^{2} + {3}^{2} - 6} = \sqrt{4} = 2$