Question

What is an equation of a parabola with a vertex at the origin and directrix x=4.75?

Answer 1

An equation for the parabola would be y²=-19x.

Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis.  This means we will use the standard form

(y-k)²=4p(x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.

Beginning with the directrix:

x=h-p=4.75
h-p=4.75

Since the vertex is at (0, 0), this means h=0 and k=0:

0-p=4.75
-p=4.75
p=-4.75

Substituting this into the standard form as well as our values for h and k we have:
(y-0)²=4(-4.75)(x-0)
y²=-19x