Final answer:
The equation of the ellipse is (x + 1)^2/2^2 + (y - 3)^2/4^2 = 1.
Step-by-step explanation:
Given that the vertices of the ellipse are at (1, 7) and (1, -3) and the length of the minor axis is 4, we can determine that the center of the ellipse is at (1, 2) since it is the midpoint of the y-coordinates of the vertices.
The semi-major axis of the ellipse is the distance from the center to one of the vertices on the major axis. In this case, the semi-major axis is 7 - 2 = 5.
The equation of an ellipse is given by (x-h)2/a2 + (y-k)2/b2 = 1, where (h, k) is the center of the ellipse, a is the semi-major axis, and b is the semi-minor axis.
Substituting the values into the equation gives us (x-1)2/52 + (y-2)2/22 = 1. Therefore, the correct equation is D. (x + 1)2/22 + (y - 3)2/42 = 1.