Answer
The given equation represents a circle with:
center at $(-\frac{1}{4}, -1)$
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:
$\\(x^2+\frac{1}{2}x)+(y^2+2y)=-\frac{1}{16}
\\(x^2+\frac{1}{2}x+\frac{1}{16})+(y^2+2y+1)=-\frac{1}{16} + \frac{1}{16}+1
\\(x+\frac{1}{4})^2+(y+1)^2=1$
Thus, the given equation represents a circle with center at $(-\frac{1}{4}, 1)$ and a radius of $1$ unit.
