Answer:
The equation for an ellipse centered at the origin with foci at (-3, 0) and (+3, 0) and co-vertices at (0, -4) and (0, +4) is:

Step-by-step explanation:
An ellipse center at origin is modelled after the following expression:

Where:
,
- Major and minor semi-axes, dimensionless.
The location of the two co-vertices are (0, - 4) and (0, + 4). The distance of the major semi-axis is found by means of the Pythagorean Theorem:
![2\cdot b = \sqrt{(0-0)^{2}+ [4 - (-4)]^{2}}](https://tex.z-dn.net/?f=2%5Ccdot%20b%20%3D%20%5Csqrt%7B%280-0%29%5E%7B2%7D%2B%20%5B4%20-%20%28-4%29%5D%5E%7B2%7D%7D)


The length of the major semi-axes can be calculated by knowing the distance between center and any focus (c) and the major semi-axis. First, the distance between center and any focus is determined by means of the Pythagorean Theorem:
![2\cdot c = \sqrt{[3 - (-3)]^{2}+ (0-0)^{2}}](https://tex.z-dn.net/?f=2%5Ccdot%20c%20%3D%20%5Csqrt%7B%5B3%20-%20%28-3%29%5D%5E%7B2%7D%2B%20%280-0%29%5E%7B2%7D%7D)


Now, the length of the minor semi-axis is given by the following Pythagorean identity:



The equation for an ellipse centered at the origin with foci at (-3, 0) and (+3, 0) and co-vertices at (0, -4) and (0, +4) is:
