Answer
Focus: $(-\frac{1}{4},0)$ (Red point)
Directrix: $x=\frac{1}{4}$ (Black line)
![](https://gradesaver.s3.amazonaws.com/uploads/solution/4e54b058-2894-4b31-972e-bd33a80edc86/result_image/1564452342.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015216Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=391c4e2c77805661a71eaafea929d9b3524cace4997d97225f8f48cae32689af)
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: $x=-p=\frac{1}{4}$