Parabolas: Directrix, Focus and Vertex

Write the parabola as $x = ay^2$ or $y = ax^2$. The focal distance is $p = \frac{1}{4a}$.

For $x = ay^2$ the parabola opens along the $x$-axis: the focus sits at $(p, 0)$ and the directrix is the line $x = -p$. For $y = ax^2$ it opens along the $y$-axis: focus $(0, p)$, directrix $y = -p$.

So for $x = y^2$, $a = 1$ and $p = \frac{1}{4}$, giving directrix $x = -\frac{1}{4}$. The only real work is inverting $4a$.