Final answer:
The directrix of the parabola described by the equation x = 8y is none of the given options. The correct directrix should be x = -1/32, which is not listed. There seems to be a typo in the question or the provided answer choices.
Step-by-step explanation:
The student is asking about the directrix of the parabola defined by the equation x = 8y. First, we should note that this is a horizontal parabola, which opens to the right if 8 is positive or to the left if 8 is negative. For a parabola that opens horizontally, the general form is (y - k)^2 = 4p(x - h), where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus and also from the vertex to the directrix.
Comparing x = 8y with the general form, we get y^2 = 1/8x, which implies that 4p = 1/8, so p = 1/32. Since the parabola opens to the right (positive x direction), and our vertex is at the origin (0, 0), the directrix will be a vertical line to the left of the vertex. Therefore, it will have the equation x = -p, so the directrix is x = -1/32. However, this is not one of the given options, so it looks like there may have been a typo in the question or the options provided. Among the given options, none match the correct directrix of x = -1/32, which is closest to option C, but note that the correct value of the constant is -1/32, not -1/8.