Answer:
[tex]y^2=-8x[/tex]
Step-by-step explanation:
If a focus of the parabola is placed to the left from the vertex, then the standard equation of the parabola is
[tex]y^2=-2px,[/tex]
where p is the distance from the focus to the directrix or [tex]\frac{p}{2}[/tex] is the distance from the focus to the vertex.
Thus,
[tex]\dfrac{p}{2}=\sqrt{(-2-0)^2+(0-0)^2}=2\\ \\p=4[/tex]
Therefore, the equation of the parabola is
[tex]y^2=-8x[/tex]
