Question

Find the coordinates of the focus, axis of the parabola ,the equation of directrix and the length of the latus rectum for $x{}^2=-9y$

Answer 1

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 $=(0,-a)=(0,-\frac{9}{4})$
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 $=4a=9$