Answer
Focus: $(-\frac{3}{2},0)$ (Red point)
Directrix: $x=\frac{3}{2}$ (Black line)
Work Step by Step
Parabola in the standard form with the vertex at origin (horizontal axis):
$y^2=4px$
$y^2=-6x$
That is:
$4px=-6x$
$p=-\frac{3}{2}$
$(p,0)=(-\frac{3}{2},0)$
Directrix: $x=-p=\frac{3}{2}$
