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 [tex](x-2)^2.[/tex]
We equate that to the squared distance of (x,y) to the focus (-2,0):
[tex](x-2)^2 = (x - -2)^2 + (y - 0)^2[/tex]
[tex]x^2 -4x + 4=x^2 +4x +4 + y^2[/tex]
[tex]-8x = y^2[/tex]
We could call that done. A more standard form might be
[tex]x =- \dfrac 1 8 \ y^2[/tex]
