# How do you graph x² + y² - 2x - 8y + 16 =0?

Feb 17, 2016

circle: centre (1 , 4 ) , r = 1

#### Explanation:

The general equation of a circle is

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

${x}^{2} + {y}^{2} - 2 x - 8 y + 16 = 0 \text{ is in this form }$

and by comparison of the 2 equations

2g = -2 → g = -1 , 2f = - 8 → f = - 4 and c = 16

centre = ( - g , -f ) = ( 1 , 4 )

and $r = \sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{\left(- 1\right)}^{2} + {\left(- 4\right)}^{2} - 16} = 1$