Final answer:
The focus is at (5, 3) and the directrix is y = -3.
Step-by-step explanation:
The given equation (x - 5)² = 12y represents a parabola in standard form. To identify the focus and directrix, we need to rewrite the equation in the form (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus.
In this case, h = 5, k = 0, and 4p = 12. By solving for p, we find that p = 3. Therefore, the focus is at (5, 3) and the directrix is the horizontal line y = -3.