Final answer:
To write the equation of a parabola using the distance formula, we first need to find the vertex of the parabola. The vertex is located at the midpoint between the focus and the directrix. The equation of the parabola is x^2 = -28y.
Step-by-step explanation:
To write the equation of a parabola using the distance formula, we first need to find the vertex of the parabola. The vertex is located at the midpoint between the focus and the directrix. In this case, the focus is (0, -7) and the directrix is y = 7. The y-coordinate of the vertex will be the average of the y-coordinate of the focus and the y-coordinate of the directrix, which is (-7 + 7)/2 = 0. Therefore, the vertex of the parabola is (0, 0).
Next, we can use the vertex form of the equation of a parabola, which is (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus (or the vertex and the directrix if p is negative).
Since the vertex is (0, 0) and the directrix is y = 7, we know that p = -7. Plugging these values into the vertex form, we get the equation of the parabola as x^2 = -28y.