The equation of the parabola whose focus is at (7, 0) and directrix at x = -7 is:

The directrix x=-7 must be perpendicular to the axis that goes through the focus (7,0), then the axis of this parabola is y=0
The directrix cuts the axis of the parabola at the point (-7,0)

The vertex of the parabola V=(h,k) is the midpoint of the points (-7,0) and (7,0=
h=(-7+7)/2=(0)/2→h=0
k=(0+0)/2=(0)/2→k=0
Vertex: V=(h,k)→V=(0,0)

As the axis of the parabola is horizontal, the parabola has an equation of the form:
(y-k)^2=4p(x-h)

The parabola opens to the right then p is positive (p>0)
p is the distance between the vertex and the focus, the p=7

(y-k)^2=4p(x-h)
(y-0)^2=4(7)(x-0)
y^2=28x

  The equation of the parabola whose focus is at (7, 0) and directrix at x = -7 is: y^2=28x

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