Question

Find the coordinates of the focus, the 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 obtain
$-4a = -9$

$a = -9/-4 = 9/4$
∴ Coordinates of the focus $=(0,-a) = (0, -9/4)$
Since the given equation involves $x^2$ ,

the axis of the parabola is the y-axis.
Equation of directrix $y = a,$

then,$y = 9/4$

Length of latus rectum = $4a = 4(9/4) = 9$ (Ans)