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

so the focus is at (7, 0), the directrix in a parabola is equidistant from the vertex to the focus
that is, the same distance from the vertex to the focus, is the distance from the vertex to the directrix

so the directrix is at x= -7

notice the focus is to the right side of the origin
and the directrix is to the left side

that means the parabola is opening horizontally

half-way between the directrix and the focus is, of course the vertex
between x = 7 and x =-7, the half-way is the origin, (0, 0)

so the center is at (0, 0)

so the parabola looks like