Chapter 9 Quadratic Relations and Conic Sections - 9.4 Graph and Write Equations of Ellipses - 9.4 Exercises - Skill Practice - Page 637: 30

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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 $(\pm a,0)$ is the vertex and $(0,\pm b)$ is the co-vertex. Thus, we find: $$\frac{x^2}{(-3\sqrt 5)^2}+\frac{y^2}{(\pm 9)^2}=1$$ $$\frac{x^2}{45}+\frac{y^2}{81}=1$$