Final answer:
The vertices of the ellipse given by (x+2)^2/16 + (y-2)^2/25 = 1 are at (-2, 7) and (-2, -3), which means the correct answer is Option A.
Step-by-step explanation:
The question pertains to determining the vertices of an ellipse given in the form (x+2)2/16 + (y-2)2/25 = 1. An ellipse is a closed curve that can be defined as the set of all points for which the sum of the distances from two fixed points (the foci) is constant.
The given equation of the ellipse resembles the standard form (x-h)2/a2 + (y-k)2/b2 = 1, where the center is at (h, k), a2 is the denominator under the x-term, and b2 is the denominator under the y-term. In this case, the center of the ellipse is at (-2, 2). The length of the major axis is 2a and the length of the minor axis is 2b.
The major axis of the ellipse is along the y-axis since 25 > 16. Therefore, a2 = 25 and a = 5. The vertices on the major axis are at C ± a units from the center along the y-axis. Substituting the values, we get the vertices at (-2, 2+5) and (-2, 2-5), which simplifies to (-2,7) and (-2,-3) respectively. Hence, the correct answer is Option A.