Question:
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for $x^{2}=-9 y$
Solution:
The given equation is $x^{2}=-9 y$.
Here, the coefficient of y is negative. Hence, the parabola opens downwards.
On comparing this equation with $x^{2}=-4 a y$, we obtain
$-4 a=-9 \Rightarrow b=\frac{9}{4}$
$\therefore$ Coordinates of the focus $=(0,-a)=\left(0,-\frac{9}{4}\right)$
Since the given equation involves $x^{2}$, the axis of the parabola is the $y$-axis.
Equation of directrix, $y=a$, i.e., $y=\frac{9}{4}$
Length of latus rectum $=4 a=9$