Question:
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for $x^{2}=-16 y$
Solution:
The given equation is $x^{2}=-16 y$.
Here, the coefficient of y is negative. Hence, the parabola opens downwards.
On comparing this equation with $x^{2}=-4$ ay, we obtain
$-4 a=-16 \Rightarrow a=4$
$\therefore$ Coordinates of the focus $=(0,-a)=(0,-4)$
Since the given equation involves $x^{2}$, the axis of the parabola is the $y$-axis.
Equation of directrix, $y=$ a i.e., $y=4$
Length of latus rectum $=4 a=16$