Write an equation of a parabola with a vertex at the
origin and a directrix at y = 5.
Since the directrix is y = 5, the distance from the vertex to the focus (which is also the distance from the vertex to the directrix) is 5 units.
Since the vertex is at the origin, the focus is at (0, -5).
The equation of a parabola with vertex at the origin and focus (0, -5) is:
y = -1/(4p) * x^2
where p = -5 and the negative sign indicates that the parabola opens downwards.
Thus, the equation of the parabola is:
y = -1/20 * x^2