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

Have you solved these types of problems before?

Answer 2

i got y^2=-12x

Answer 3

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. Are you with me? And no. That's incorrect.

Answer 4

yes got it so far @YanaSidlinskiy

Answer 5

Ok. So what we do next is:
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)
The parabola looks like this:
so the "focus form" equation for a parabola opening is (y−k)^2=4p(x−h)
the vertex is at (h, k)
p = distance from the vertex to the focus
p > 0, opens to the right
p < 0, opens to the left