The equation of the directrix of the parabola $x^2+8x+12y+4=0$ is

For the parabola $y^2+6y-2x=-5$,consider the following statements:
$I$. The vertex is $(-2, -3)$.
$II$. The directrix is $y+3=0$.
Which of the following is correct?

If $a > 0$ and $b^2 - 4ac = 0$,then the curve $y = ax^2 + bx + c$

The distance of the point $(6, -2 \sqrt{2})$ from the common tangent $y = mx + c$ $(m > 0)$ of the curves $x = 2y^2$ and $x = 1 + y^2$ is

If the length of the latus rectum of a parabola,whose focus is $(a, a)$ and the tangent at its vertex is $x+y=a$,is $16$,then $|a|$ is equal to.

If $P$ and the origin are the points of intersection of the parabolas $y^2=32x$ and $2x^2=27y$,and if $\theta$ is the acute angle between these curves at $P$,then $5\sqrt{\tan \theta} =$