Chapter 9 Quadratic Relations and Conic Sections - 9.4 Graph and Write Equations of Ellipses - 9.4 Exercises - Skill Practice - Page 638: 37

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Given: $25x^2+81y^2=2025$ Rewrite as $\frac{x^2}{81}+\frac{y^2}{25}=1$ We can see $a=9, b=5$ The denominator of the $x^2-term$ is bigger than that of the $y^2-term$, so the major axis is vertical. The vertices of the ellipse are at $(\pm a,0)=(\pm 9,0)$. The co-vertices are at $(0,\pm b) = (0,\pm 5)$.