Chapter 11: Parametric Equations and Polar Coordinates - Section 11.6 - Conic Sections - Exercises 11.6 - Page 677: 4

$x^{2}=2y$ Focus$:\displaystyle \qquad (0,\frac{1}{2})$ Directrix: $\displaystyle \qquad y=-\frac{1}{2}$

The parabola opens up: $\quad\Rightarrow \quad x^{2}=4py$ The only equation of this form is $x^{2}=2y=4(\displaystyle \frac{1}{2})x,\qquad\Rightarrow p=\frac{1}{2}$ Focus is at $(0,p)=(0,\displaystyle \frac{1}{2})$ Directrix is: $\qquad $ $y=-p$ $y=-\displaystyle \frac{1}{2}$