# How do you graph x^2+y^2+3x-6y+9=0?

Mar 5, 2016

circle : centre$\left(- \frac{3}{2} , 3\right) , \text{ radius } = \frac{3}{2}$

#### Explanation:

The general form of the equation of a circle is :

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

centre = (-g,-f) and r = $\sqrt{{g}^{2} + {f}^{2} - c}$

${x}^{2} + {y}^{2} + 3 x - 6 y + 9 = 0 \text{ is in this form }$

and by comparison : 2g = 3 → g $= \frac{3}{2}$, 2f = -6 → f = -3, c=9

centre = $\left(- \frac{3}{2} , 3\right) \text{ and } r = \sqrt{{\left(\frac{3}{2}\right)}^{2} + {\left(- 3\right)}^{2} - 9} = \frac{3}{2}$