Chapter 9 Quadratic Relations and Conic Sections - 9.4 Graph and Write Equations of Ellipses - 9.4 Exercises - Skill Practice - Page 637: 27

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We know the following equation for an ellipse centered at the origin: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ Where $(0,\pm a)$ is the vertex and $(\pm b,0)$ is the co-vertex. Thus, we find: $$\frac{x^2}{(\pm 2)^2}+\frac{y^2}{(-4)^2}=1$$ $$\frac{x^2}{4}+\frac{y^2}{16}=1$$