Answer
The equation represents a circle
$ (x+0)^2+(y^2+3)^2=(\sqrt{7})^2$
with center $(0,-3)$ and radius is $\sqrt{7}$
Work Step by Step
$\underline{\textbf{Given equation}}$
$x^2+y^2+6y+2=0$
$\Rightarrow x^2+y^2+6y=-2$
$\Rightarrow x^2+y^2+6y=-2$
$\Rightarrow (x^2)+(y^2+6y)=-2$
$\Rightarrow (x^2)+(y^2+6y+9)=-2+9$
$\Rightarrow (x+0)^2+(y^2+3)^2=(\sqrt{7})^2$
Which is the standard form for the equation of circle with center $(0,-3)$ and radius is $\sqrt{7}$
