Final answer:
The equation of the parabola is (x + 7)² = 32(y + 3).
Step-by-step explanation:
The equation of a parabola with a focus at (-7,5) and a directrix of y = -11 can be derived using the formula:
(x - h)² = 4p(y - k)
Where (h, k) represents the vertex and p represents the distance between the vertex and either the focus or the directrix.
Since the directrix is a horizontal line, the vertex is (h, k) = (-7, -3).
The distance between the vertex and the directrix is p = 8.
Substituting these values into the formula, we get:
(x + 7)² = 32(y + 3)
So, the equation of the parabola is (x + 7)² = 32(y + 3).