Answer
The given equation represents a circle with:
center at (-2, 3)
radius = 1 unit
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:
$\\(x^2+4x)+(y^2-6y)=-12
\\(x^2+4x+4)+(y^2-6y+9) = -12+4+9
\\(x+2)^2 + (y-3)^2=1$
Thus, the given equation represents a circle with center at (-2, 3) and a radius of 1 unit.