Question

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

Answer 1

$x^2=-16y$

Here, the coefficient of y is negative, hence, the parabola opens downwards.

On comparison with $x^2=-4ay$

$-4a=-16$

$a=4$

Coordinates of the focus $(0,-4)$.

Since the given equation involves $x^2$, the axis of the parabola is y-axis.

Equation of directrix, $y=a$ i.e., $y=4$

Length of latus rectum = $4a=16$

'