Final answer:
The parabola with a focus at (8,-5) and a directrix at y = 1 has a vertex at (8, -2), a p-value of 3, and opens downwards, which is not listed in the provided options.
The correct option is not given.
Step-by-step explanation:
The question asks about the properties of a parabola given a focus at (8,-5) and a directrix of y = 1. To determine the properties, we need to find the vertex and decide the direction in which the parabola opens. The vertex lies exactly between the focus and the directrix. We can find the y-coordinate of the vertex by averaging the y-coordinates of the focus and the directrix.
Thus, the y-coordinate of the vertex is (-5 + 1) / 2 = -2. Since the focus has a more negative y-coordinate than the directrix, the parabola opens downward. The distance from the vertex to the focus or the directrix is the value of p. The vertex is 3 units from the directrix and also 3 units from the focus, so the p-value is 3.
Therefore, the correct answer is none of the stated options. The parabola has a vertex at (8, -2) and has a p-value of 3, opening downwards.
The correct option is not given.