How to identify properties of conic $12x+y^2-6y+45=0$ 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.

Hints and References :  


*

*Look up the detailed guide here.  

*The parabola is shifted and it is rotated by 180 degrees . ( The -ve sign of p indicates that it has been flipped)  

*This might also help.

