Question

Write an equation of a parabola that opens to the left, has a vertex at the origin, and a focus at (–9, 0.

Answer 1

The standard equation of parabola:

(y-k)²=4p(x-h), with:

a) vertex = (h,k)

b) focus = (h+p, k)

c) directrix = (x=h-p)


Since this parabola has a vertex at (0,0) that means h=k=0

Hence the equation becomes: y²=4px, let's calculate p:
focus is given (-9,0) Remember h+p = -9 & since h=0, then p= -9
===> y²= - 36x