Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line. f(–2, 0); x = 2

The line is called the directrix.  Here we have a vertical directrix, so a parabola sideways from usual.

Geometry is best done with squared distances.  The squared distance from an arbitrary point (x,y) to the vertical line x=2 is 

We equate that to the squared distance of (x,y) to the focus (-2,0): 







We could call that done.  A more standard form might be