Question

Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7

Answer 1

I got x = 1/28 y2

Answer 2

the distance from the vertex to the focus is EXACTLY the same as from the vertex to the directrix

the focus is in the direction where the parabola opens up
the directrix is in the opposite side of the focus


so as you can see, the parabola is opening up to the right
the vertex is half-way between the focus and the directrix, thus at the origin in this case
the "focus form" for a parabola opening horizontally is \(\bf (y-k)^2=4p(x-h)\)

(h, k) = vertex coordinates
p = distance from the vertex to the focus [ or directrix for that matter ]

if it opens to the right, the "p" is positive
if it opens to the left, the "p" is negative