What are the focus and directrix of the parabola with the given equation x=-1/8y^2?

The parabola y²=4px has vertex (0,0), focus (0, p) and the equation of the diretrix x=-p.

from our expression:

x=-1/8y²

multiply through by - 8 we get:

-8x=y²

copmaring to

y²=4px

4p=-8

p-2

so it has vertex (0,0), focus (p, 0) = (-2,0)

equation of directrix x=-p, or x=2

equation of the axis of symmetry y=0