Question

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

Answer 1

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