Answer:
[tex]y^2=-8x[/tex]
Step-by-step explanation:
The directrix intersects the x-axis at point (2,0). Points (-2,0) and (2,0) are symmetric about the origin, so the vertex of the parabola is placed at the origin (0,0).
The parameter p of the parabola is the distance from the focus to the directrix, thus p=4.
The branches of the parabola go in negative direction of x-axis, because the focus lies to the left from the vertex.
The equation of the parabola is
[tex](y-0)^2=-2\cdot 4\cdot (x-0),\\ \\y^2=-8x.[/tex]
