Question

Find the coordinates of the focus axis of the parabola, the equation of directrix and the length of the latus rectum for the parabola $x{}^2$ $=-16y$.

Answer 1

The given equation is $x^2=-16y$
Here, the coefficient of $y$ is negative.
Hence the parabola opens downwards.
On comparing this equation with $x^2=-4ay$
$-4a=-16$
$\Rightarrow a=4$
$\therefore$ Coordinates of the focus $=(0,-a)=(0,-4)$
Axis of the parabola is the $y$-axis i.e $x=0$
Equation of directrix $y=a$ i.e., $y=4$
Length of latus rectum $=4a=16$