Final answer:
The equation of the parabola is (x + 4)² = 4(y - 6). The focus is located at (-4, 5) and the directrix is y = 7. Graphing the parabola involves plotting the focus and drawing a line parallel to the directrix.
Step-by-step explanation:
To find the equation of a parabola with a focus at (-4, 5) and a directrix at y = 7, we can use the formula for a parabola in vertex form: (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and either the focus or directrix.
In this case, the vertex is (-4, 6) because it is the midpoint between the focus and the directrix. The distance from the vertex to the focus or directrix is 1, so p = 1.
Substituting these values into the equation gives us: (x + 4)² = 4(y - 6) as the equation of the parabola.
To graph the parabola, we can plot the focus at (-4, 5) and draw a line parallel to the directrix at y = 7.