Answer
The given equation represents a circle witih:
center at $(\frac{1}{4}, -\frac{1}{4})$
radius = $\frac{1}{2}$
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:
$\\(x^2-\frac{1}{2}x)+(y^2+\frac{1}{2}y)=\frac{1}{8}
\\(x^2-\frac{1}{2}x+\frac{1}{16})+(y^2+\frac{1}{2}y+\frac{1}{16})=\frac{1}{8} + \frac{1}{16}+\frac{1}{16}
\\(x-\frac{1}{4})+(y+\frac{1}{4})^2=\frac{2}{16}+\frac{1}{16}+\frac{1}{16}
\\(x-\frac{1}{4})+(y+\frac{1}{4})^2=\frac{1}{4}$
Thus, the given equation represents a circle with center at $(\frac{1}{4}, -\frac{1}{4})$ and a radius of $\frac{1}{2}$ units.