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.

Yes, this is a parabola. You can factor out like this: 
$$(y-3)^2 = -12(x+3)$$
This means, the vertex is located at $(-3,3)$. The parabola is opening towards the left. 
In this case, $-4p = -12$, $p=3$. This means the distance from focus to vertex is 3. If you draw the parabola, the focus should be located at $(-6,3)$. The directrix should be a vertical line with the nearest point to the vertex also having a distance of 3. Hence, directrix is $x=0$. 
