Chapter 9 Quadratic Relations and Conic Sections - 9.4 Graph and Write Equations of Ellipses - 9.4 Exercises - Skill Practice - Page 637: 2

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Consider two possible conditions. (1) If an ellipse has the vertices at $(\pm a,0)$ and the co-vertices at $(0,\pm b)$, then the foci are at $(\pm c,0)$ where $c^2=a^2-b^2$. (2) If an ellipse has the vertices at $(0, \pm b)$ and the co-vertices at $(\pm a,0)$, then the foci are at $(0, \pm c)$ where $c^2=b^2-a^2$.