Answer
The equation represents a circle
$ (x+1)^2+(y^2+\frac{1}{2})^2=(\frac{1}{2})^2$
with center $(-1,-\frac{1}{2})$ and radius is $\frac{1}{2}$
Work Step by Step
$\underline{\textbf{Given equation}}$
$x^2+y^2+2x+y+1=0$
$\Rightarrow x^2+y^2+2x+y=-1$
$\Rightarrow x^2+2x+y^2+y=-1$
$\Rightarrow (x^2+2x)+(y^2+y)=-1$
$\Rightarrow (x^2+2x+1)+(y^2+y+\frac{1}{4})=-1+1+\frac{1}{4}$
$\Rightarrow (x+1)^2+(y+\frac{1}{2})^2=(\frac{1}{2})^2$
Which is the standard form for the equation of circle with center $(-1,-\frac{1}{2})$ and radius is $\frac{1}{2}$
