Question

Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.

Answer 1

Standard form is, hold a sec

x=2 is directix
that means it opens left or right
so we must use
(y-k)²=4p(x-h)
where vertex is (h,k) and p is distance from focus to vertex
also shortest distance from vertex to directix
the shortest distance from focus to directix is 2p
if p>0 then the parabola opens right
if p<0 then pareabola opens left

so
(-2,0) and x=2
the distance is 4
4/2=2
p=2
wait, positive or negative
focus is to the left of the directix so p is negative
p=-2

vertex is 2 to the right of the focus and 2 to the left of directix
vertex is (0,0)

so
(y-0)²=4(-2)(x-0) or
y²=-8x is da equation
not sure what form is standard tho