219. Determine the coordinates of the focus of the parabola $y=-\frac{1}{6} x^{2}$ and write the equation of its directrix.
Solution. We write the given equation of the parabola in canonical form as $x^{2}=-6 y$. By comparing this equation with equation (7), we get $2 p=-6, p=-3$. Therefore, the focus of the parabola is at the point $F(0; -1.5)$ and the equation of the directrix $DE y=1.5$.