Final answer:
The focus of the parabola with the given equation (y-3)^2 = -4(x-5) is at point (4, 3), and the directrix is the line x = 6. None of the answer choices are correct.
Step-by-step explanation:
The equation given is (y-3)^2 = -4(x-5). This is a standard form of the equation for a parabola that opens to the left since the coefficient of the (x-5) term is negative and the squared term is (y-3)^2. To find the focus and directrix of the parabola, we note that the general form of a parabola opening to the left or right is (y-k)^2 = 4p(x-h), where the point (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus and to the directrix. In the given equation, h = 5 and k = 3, so the vertex is (5, 3). The value of p can be determined by comparing the given equation to the general form, which reveals p = -1. Therefore, the focus, located p units to the left of the vertex, is at (4, 3). The directrix is a vertical line, located p units to the right of the vertex, hence it is the line x = 6. We can discard the other options as they do not match the calculated values for the focus.