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

X=-1/8y^2

If the Vertex is at the origin: V = (h, k) = (0,0) →h=0, k=0

y^2=4px

(-8) (x=-1/8y^2)

-8x=y^2

y^2=-8x

4p=-8

Solving for p:

4p/4=-8/4

p=-2<0 (negative) →The parabola opens to the left

Focus: F = (p, 0) →F = (-2,0)

Drectrix: x=-p = - (-2) →Directrix: x=2

Answers:

Focus = (-2,0)

Directrix: x=2