The given equation is $x^2=-9y$
Here the coefficient of $y$ is negative.
Hence, the parabola opens downwards
On comparing this equation with $x^2=-4ay$, we get 
$-4a=-9$
$\Rightarrow a=\frac{9}{4}$
$\therefore$ Coordinates of the focus $=(0,-a)=\left(0,-\frac{9}{4}\right)$
Axis of the parabola is the $y$-axis i.e $x=0$
Equation of directrix $y=a$  i.e. $y=\frac{9}{4}$
Length of latus rectum $=4a=9$