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 .