Answer
Focus: $(-\frac{1}{4},0)$ (Red point)
Directrix: $x=\frac{1}{4}$ (Black line)
Work Step by Step
Parabola in the standard form with the vertex at origin (horizontal axis):
$y^2=4px$
$x+y^2=0$
$y^2=-x$
That is:
$4px=-x$
$p=-\frac{1}{4}$
$(p,0)=(-\frac{1}{4},0)$
Directrix: $x=-p=\frac{1}{4}$
