Question

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

Answer 1

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