Question

Find the vertex, focus, directrix, and focal width of the parabola: -1/40x^2=y

Answer 1

for
(x-h)^2=4p(y-k)
vertex is (h,k)
distance from vertex to directix=p=distance from vertex to focus
|4p|=focal width

remember, focus is on the side of the parabola where it opens and directix is at the back
when p is negative, it opens down
when p is positive, it opens up

look at equation
-1/40(x-0)^2=(y-0)
times -40 to both sides
(x-0)^2=-40(y-0)
(x-0)^2=4(-10)(y-0)
vertex=(0,0)
p=-10,it's negative so it opens down

focus is 10 units below vertex (y direction)
focus=(0,-10)

diretix is 10 above
directix is y=10

focal width=|4p|=|4(-10)|=|-40|=40




vertex=(0,0)
focus=(0,-10)
directix is y=10
focal width=40 units