To solve this problem, we can start with the general equation for an ellipse that has its major axis parallel to the y-axis:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1.
Here, (h, k) represents the coordinates of the center of the ellipse, 'a' is the length of the semi-major axis, and 'b' is the length of the semi-minor axis.
In the given problem, the center of the ellipse is at the origin, i.e. (h, k) = (0, 0). Hence, we can simplify the general equation to:
x^2/a^2 + y^2/b^2 = 1.
Further, it's given that the foci of the ellipse lie at (0, 4) and (0, -4). The distance from the center of an ellipse to its foci along the major axis is given by the absolute value of 'b'.
Therefore, we conclude that the length of the semi-minor axis, 'b', is equal to 4.
Again, the vertices of the ellipse are given as (0, 7) and (0, -7). The distance from the center of an ellipse to its vertices along the major axis is represented by 'a'.
By comparing this with the provided coordinates, we determine that the length of the semi-major axis, 'a', is 7.
Substituting the values of 'a' and 'b' into the simplified equation, we get
x^2/49 + y^2/16 = 1.
So, the equation of the given ellipse is x^2 / 49 + y^2 / 16 = 1.