Chapter 9 Quadratic Relations and Conic Sections - 9.5 Graph and Write Equations of Hyperbolas - 9.5 Exercises - Quiz for Lessons 9.4-9.5 - Page 648: 5

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If the vertex of an ellipse is at $(0,\pm a)$ and the co-vertex is at $(\pm b,0)$, then the equation of the ellipse is: $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ Find $b^2=a^2-c^2=10^2-8^2=36\\ \rightarrow b=\pm 6$ Hence here $a=10,b=6$ Thus the equation is: $\frac{x^2}{100}+\frac{y^2}{36}=1$