I need to find out the type of conic, the coordinates of the center, focus (foci), vertex (vertices), directrix for the conic given by:

$$12x+y^2-6y+45=0$$

I completed the square to get

$$(y-3)^2+36=-12x$$

This is a parabola I believe since it is of the form $y^2=4px$ which is a parabola rotated by $\frac{\pi}{2}$ clockwise if I'm not mistaken.

I am now struggling on how to get the rest of this information so any help is appreciated.