#### Answer

$$\frac{x^2}{400}+\frac{y^2}{256}=1$$

#### Work Step by Step

We know the following equation for an ellipse centered at the origin:
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
Where $(a,0)$ is the vertex and $(b,0)$ is the co-vertex.
Thus, we find:
$$\frac{x^2}{(20)^2}+\frac{y^2}{(-16)^2}=1$$
$$\frac{x^2}{400}+\frac{y^2}{256}=1$$