Final answer:
The parabola has its focus at (5, 0) and directrix y=6, which means it opens downward with a vertex at (5, 3). Its equation will be in the form y = -a(x - 5)² + 3, where a is a negative value reflecting the downward opening of the parabola.
Step-by-step explanation:
The question asks about the properties of a parabola given the focus at (5, 0) and the directrix at y = 6. A parabola is the set of all points that are equidistant from the focus and the directrix. In this case, since the directrix is a horizontal line and the focus has a y-coordinate of 0, the parabola will open vertically. Since the focus is below the directrix, we know the parabola opens downward. The vertex of the parabola will be halfway between the focus and the directrix, so here the vertex will be at (5, 3). The general equation of a parabola in vertex form is y = a(x - h)² + k where (h, k) is the vertex. As (h, k) is (5, 3) for this parabola, and it opens downward (indicating a is negative), the equation will have a form similar to y = -a(x - 5)² + 3, where the exact value of a determines the 'width' or 'steepness' of the parabola.