# How do you graph x^2+y^2+2x+2y=23?

Feb 15, 2016

Just draw a circle with center at $\left(- 1 , - 1\right)$ and radius $5$.

#### Explanation:

General form of quadratic equation of a conic section is $a {x}^{2} + b {y}^{2} + 2 h x y + 2 g x + 2 f y + c = 0$.

As in given the equation ${x}^{2} + {y}^{2} + 2 x + 2 y = 23$, the term $x y$ is not there and coefficients of ${x}^{2}$ and ${y}^{2}$ are equal, this is the equation of a circle.

${x}^{2} + {y}^{2} + 2 x + 2 y = 23$

$\Leftrightarrow$ $\left({x}^{2} + 2 x + 1\right) + \left({y}^{2} + 2 y + 1\right) = 23 + 1 + 1$

$\Leftrightarrow$ $\left(x + {1}^{2}\right) + {\left(y + 1\right)}^{2} = 25 = {5}^{2}$

As this is the equation of a circle with center at $\left(- 1 , - 1\right)$ and radius $5$.

Hence to draw the graph of ${x}^{2} + {y}^{2} + 2 x + 2 y = 23$, draw a circle with center at $\left(- 1 , - 1\right)$ and radius $5$