Question

Find the coordinates of focus, the equation of the directrix and length of the latus rectum of the conic represented by the equation $x^2=-16y$

Answer 1

The given equation is $x^2=-16y$ ..........$\left(1\right)$

which is comparable with $x^2=-4ay$, so $\left(1\right)$ represents a parabola of the standard form.

Here $4a=16\Rightarrow a=4$

$\therefore$The focus is $(0,-a)=(0,-4)$ and the equation of the directrix is $y-a=0$

$\Rightarrow y-4=0$

The length of the latus rectum$=4a=4\times 4=16$