Answer:
[tex]x^2+6x+6y=0[/tex]
Step-by-step explanation:
The distance between the parabola focus and the directrix is 3, then
[tex]p=3.[/tex]
Parabola vertex is placed on the perpendicular line to the directrix and this perpendicular line passes trough the focus. Its equation is x=-3 and parabola vertex coordinates are (-3,1.5).
Branches of the parabola go in negative y-direction, then the equation of the parabola is
[tex](x-(-3))^2=-2\cdot 3(y-1.5),\\ \\(x+3)^2=-6(y-1.5),\\ \\x^2+6x+9=-6y+9,\\ \\x^2+6x+6y=0.[/tex]
