Chapter 11: Parametric Equations and Polar Coordinates - Section 11.6 - Conic Sections - Exercises 11.6 - Page 677: 3

$x^{2}=-6y$ Focus$:\displaystyle \qquad (0,-\frac{3}{2})$ Directrix is $\displaystyle \qquad y=\frac{3}{2}$

The parabola opens down: $\quad\Rightarrow \quad x^{2}=-4py$ The only equation of this form is $x^{2}=-6y=-4(\displaystyle \frac{3}{2})x,\qquad\Rightarrow p=\frac{3}{2}$ Focus is at $(0,-p)=(0,-\displaystyle \frac{3}{2})$ Directrix is: $y=p$ $y=\displaystyle \frac{3}{2}$