Answer
Focus: $(-\frac{3}{2},0)$ (Red point)
Directrix: $x=\frac{3}{2}$ (Black line)
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3b649967-b5d9-489c-af25-5eb028b39f03/result_image/1564451837.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020240Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=e9640477b353f292704dff2ac5f3152a4482a5beef77744c52d1f0a8c9872b72)
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: $x=-p=\frac{3}{2}$