Equation of a parabola is simplest if vertex is at origin & directrix is along x- axis or y-axis.
Four possible options for directrix, given vertex is at origin:( x = a, x =-a, y = a, y =-a).
Observations
1. Parabola is symmetric with respect to the axis of the parabola. If the equation has a y 2 term, then the axis of symmetry is along the x-axis and if the equation has an x 2 term, then the axis of symmetry is along the y-axis.