# How do you graph x^2 + y^2 + 4x - 4y - 1 = 0?

Feb 15, 2016

circle: centre =(-2 ,2) , r = 3

#### Explanation:

The general equation of a circle is

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

the equation here : ${x}^{2} + {y}^{2} + 4 x - 4 y - 1 = \text{0 is in this form}$

by comparison: 2g = 4 → g = 2 , 2f = -4 → f=-2 and c = -1

centre = (-g , -f) = (-2 , 2)

and r$= \sqrt{{g}^{2} + {f}^{2} - c} = \sqrt{{2}^{2} + {\left(- 2\right)}^{2} + 1} = \sqrt{9} = 3$