Finding the focus and directrix of the parabola $x^2=-8y$

Question

If the equation of a parabola is $x^2 = -8y$. Find the coordinates of the focus and the equation of the directrix.

I don't understand what "coordinates of the focus" means.

Answer 1

The equation of a parabola in standard form is $(x-h)^2 = 4p(y-k)$, where $(h,k)$ is the vertex. By definition, the focus of the parabola in this form is given by the coordinates $(h, k+p)$. The directrix is given by $y = k-p$. So, if your equation is $x^2 = -8y$, then setting $4p = -8$, we get $p = ?$. Once you find your $p$, it should be clear what the focus and directrix are.