Find the vertex, focus and directrix of the parabola x2=-3y

Question

Find the vertex, focus and directrix of the parabola x2=-3y

Answer 1

Greetings! Lets solve this shall we ?

So, we must find find the vertex, focus and directrix of the given parabola x² = -3y. We see that this parabola is in the form of a vertical parabola (x-h)² = 4p(y - k), where the vertex is (0,0). We now find the focus after finding p from 4p = -3. Then, p = -3/4. The focus yields (0, p) = (0, -3/4). The directrix yields y = -p, where y = -(-p) = 3/4.

I hope this helped!