# How do you graph x^2+y^2+6x-8y+9=0?

Feb 12, 2016

circle: centre(-3 , 4) and radius = 4

#### Explanation:

the general equation of a circle is

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

the equation here : ${x}^{2} + {y}^{2} + 6 x - 8 y + 9 = 0$
compares with the general equation and is therefore a circle.

by comparison of the 2 equations :

obtain: 2g = 6 → g = 3 , 2f = -8 → f = -4 and c = 9

centre = (-g , -f ) = (-3 , 4 )

and radius = $\sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{\left(- 3\right)}^{2} + {4}^{2} - 9} = \sqrt{16} = 4$