# How do you find the center and radius of the circle given x^2+y^2+2x+4y=9?

Nov 25, 2016

The center is $\left(- 1 , - 2\right)$ and the radius is $\sqrt{14} = 3.74$

#### Explanation:

The equation of a circle, center, $\left(a , b\right)$and radius $r$ is,

${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

Let's complete the squares in the above equation

${x}^{2} + 2 x + {y}^{2} + 4 y = 9$

${x}^{2} + 2 x + 1 + {y}^{2} + 4 y + 4 = 9 + 1 + 4$

${\left(x + 1\right)}^{2} + {\left(y + 2\right)}^{2} = {\left(\sqrt{14}\right)}^{2}$