Answer
The given equation represents a circle with:
center at (0, -3)
radius = $\sqrt7$ units
Work Step by Step
RECALL:
The standard form of the equation of a circle whose center is at (h, k) and radius $r$ is:
$(x-h)^2+(y-k)^2=r^2$
If the given equation can be written in the form given above, then it must represent a circle.
Rewrite the given equation by completing the square to have:
$\\x^2+(y^2+6y)=-2
\\x^2+(y^2+6y+9)=-2+9
\\x^2+(y+3)^2=7$
Thus, the given equation represents a circle with center at (0, -3) and a radius of $\sqrt7$ units.
