Step-by-step explanation:
The standard equation of a parabola is (y - k) = (1/4p)(x - h)^2, where (h,k) is the vertex and p is the distance between the vertex and the focus.
In the equation x^2 = 24y, we see that the vertex is at the origin (0,0) and the coefficient of y is 24. Therefore, p = 1/4(24) = 6.
Since the parabola opens upward, the focus is located at the point (0,p) = (0,6).
The directrix is a horizontal line that is p units below the vertex. In this case, the directrix is a horizontal line y = -6.
Therefore, the equation of the directrix of the parabola x^2 = 24y is y = -6.