# How do you graph x^2+y^2+3x+4y+4=0?

Jun 4, 2016

The graph is the circumference

${\left(x - \frac{3}{3}\right)}^{2} + {\left(y - 2\right)}^{2} = {\left(\frac{3}{2}\right)}^{2}$

#### Explanation:

${x}^{2} + {y}^{2} + 3 x + 4 y + 4 = 0$ can be represented in the form
${\left(x - {x}_{c}\right)}^{2} + {\left(y - {y}_{c}\right)}^{2} - {r}^{2} = 0$ which is the equation of the circumference with center at $\left\{{x}_{c} , {y}_{c}\right\}$ and radius $r$.
Equating coefficients we get

${x}_{c} = \frac{3}{2} , {y}_{c} = 2 , {x}_{c}^{2} + {y}_{c}^{2} - {r}^{2} = 4 \to r = \frac{3}{2}$

The graph is the circumference

${\left(x - \frac{3}{3}\right)}^{2} + {\left(y - 2\right)}^{2} = {\left(\frac{3}{2}\right)}^{2}$