Final answer:
The equation of the parabola with a given directrix x=7 is either (x - 7)^2 = 4y if the parabola opens upwards or (x - 7)^2 = -4y if it opens downwards. Without additional information about the orientation, both A and C are possible equations.
Step-by-step explanation:
The question asks us to write the equation of a parabola with a given directrix x=7. Since the directrix is vertical, the parabola opens either up or down and is of the form (x - h)^2 = 4p(y - k), where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus (or the directrix). Given that no vertex or focus is specified, and because we are not provided with the orientation of the parabola, only that the directrix is x=7, we aim to derive the possible parabola equations.
If the vertex is to the left of the directrix x=7, and the parabola opens right towards the directrix, the equation would take the form (x - 7)^2 = 4py for some positive p. However, if the parabola opens to the left, away from the directrix, the equation will have a negative coefficient, (x - 7)^2 = -4py. Without more information, we cannot determine the value of p or if the parabola opens up or down. However, because our options include only the term 4y without a k value, and assuming that the vertex lies on the y-axis, p should be 1, and the parabola opens up for option A and down for option C.