Final answer:
The correct answer is option a. The focus of the parabola represented by the equation x² = 8y is found by comparing it to the parabola's standard form. The focus is at (0, 2), corresponding to choice (a).
Step-by-step explanation:
The equation given is x² = 8y, which represents a parabola that opens upwards. To find the focus of the parabola, we can express the equation in the standard form of a parabola which is (x - h)² = 4p(y - k), where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus.
Comparing x² = 8y to the standard form, we see that h = 0 and k = 0, because the parabola is not shifted left, right, up or down from the origin. Also, 4p = 8, which means that p = 2. Hence, the focus has coordinates (0, p) because the parabola opens upwards along the y-axis.
Thus, the focus of the parabola x² = 8y is at (0, 2), which corresponds to answer choice (a).