# How do you graph x^2+y^2+8x-8y-17=0?

Feb 15, 2016

circle: centre=(-4 , 4) , r= 7

#### Explanation:

The general equation of a circle is:

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

${x}^{2} + {y}^{2} + 8 x - 8 y - 17 = \text{0 is in this form}$

by comparison: 2g = 8 → g=4 , 2f = -8 → f=-4 and c = -17

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

and $r = \sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{4}^{2} + {\left(- 4\right)}^{2} + 17} = \sqrt{49} = 7$