Chapter 10 - Parametric and Polar Curves - 10.4 Conic Sections - 10.4 Exercises - Page 750: 20

$${x^2} = - 24y$$

$$\eqalign{ & {\text{The directrix is }}y = 6,{\text{ then the parabola has the equation }}{x^2} = 4py \cr & {\text{With }}y = - p \cr & y = - p\,\,\, \Rightarrow \,\,\,\,\,p = - 6 \cr & {\text{The equation of the parabola is:}} \cr & {x^2} = 4\left( { - 6} \right)y \cr & {x^2} = - 24y \cr} $$