# How do you graph x^2+y^2+6x-2y-15=0?

Jun 3, 2016

This is the equation of a circle with center $\left(- 3 , 1\right)$ and radius $5$

#### Explanation:

As in the equation ${x}^{2} + {y}^{2} + 6 x - 2 y - 15 = 0$,

coefficients of ${x}^{2}$ and ${y}^{2}$ are equal and there is no term having $x y$ (in other words coefficient of $x y$ is $0$),

hence this is the equation of a circle.

Now ${x}^{2} + {y}^{2} + 6 x - 2 y - 15 = 0$

$\Leftrightarrow \left({x}^{2} + 6 x + 9\right) + \left({y}^{2} - 2 y + 1\right) = 15 + 9 + 1$

$\Leftrightarrow {\left(x + 3\right)}^{2} + {\left(y - 1\right)}^{2} = 5 \cdot 2$

It is therefore a circle with center $\left(- 3 , 1\right)$ and radius $5$

graph{x^2+y^2+6x-2y-15=0 [-12.42, 7.58, -3.84, 6.16]}