Write the equation of the ellipse using the given information:

The ellipse has foci (–4, 0) and (–4, 4) and vertices (–4, –1) and (–4, 5);

center is (-4,2)

c = 2
a = 3
so, b^2 = 5
and the major axis is vertical.

That help?

To write the equation of an ellipse, we need to know the coordinates of the foci and the vertices. In this case, we are given the foci (-4, 0) and (-4, 4) and the vertices (-4, -1) and (-4, 5).

First, let's determine the necessary information of the ellipse. The distance between the foci is 4 units, and the distance between the vertices is also 4 units. This implies that the major axis is vertical.

The center of the ellipse is the midpoint between the foci and is therefore (-4, (0 + 4)/2) = (-4, 2).

Next, we can determine the values of a and b, which represent half the length of the major and minor axes, respectively. In this case, a = 4 and b = 2.

The equation of an ellipse with a vertical major axis is given by:

(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

where (h, k) represents the coordinates of the center.

Plugging in the values, we get:

(x + 4)^2 / 2^2 + (y - 2)^2 / 4^2 = 1

Simplifying, we get:

(x + 4)^2 / 4 + (y - 2)^2 / 16 = 1

So, the equation of the ellipse is:

(x + 4)^2 / 4 + (y - 2)^2 / 16 = 1