For the parabola $y^2 = 4ax$ ($a > 0$), the focus and the directrix are located at:

Definition: a parabola is the locus of points equidistant from a fixed point (**focus**) and a fixed line (**directrix**). For $y^2 = 4ax$: - Focus at $(a, 0)$ — on the positive $x$-axis at distance $a$ from the vertex. - Directrix $x = -a$ — the vertical line on the *opposite* side of the vertex, also distance $a$ away. This symmetry around the vertex is the load-bearing intuition.