Chapter 9 Quadratic Relations and Conic Sections - 9.4 Graph and Write Equations of Ellipses - 9.4 Exercises - Skill Practice - Page 637: 20

$$\frac{y^2}{36}+\frac{x^2}{16}=1$$

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: $$\frac{y^2}{(-6)^2}+\frac{x^2}{(4)^2}=1$$ $$\frac{y^2}{36}+\frac{x^2}{16}=1$$