Question

Identify the focus and directrix of the following parabola
(a) 2y^2 = x
(b) x^2 = -36y

Answer 1

a) $4p(x-h)=(y-k)^2$

Focus is $(h+p,k)$

Directrix is $x=h-p$

We have:

$p=1/8, h=k=0$

focus: $(1/8,0)$

directrix: $x=-1/8$

b) $4p(y-k)=(x-h)^2$

Focus is $(h,k+p)$

Directrix is $y=k-p$

We have:

$p=-9, h=k=0$

focus: $(0,-9)$

directrix: $y=9$