Chapter 9 Quadratic Relations and Conic Sections - 9.4 Graph and Write Equations of Ellipses - 9.4 Exercises - Skill Practice - Page 637: 14

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Given: $72x^2+8y^2=648\\\frac{x^2}{9}+\frac{y^2}{81}=1$ The equation is in standard form. We can see $a=9, b=3$ The denominator of the $x^2-term$ is smaller than that of the $y^2-term$, so the major axis is vertical. The vertices of the ellipse are at $(0,\pm a)=(0,\pm 9)$. The co-vertices are at $(\pm b,0) = (\pm 3,0)$. Find the foci. $c^2=a^2-b^2=9^2-3^2=72$ so $c=6\sqrt 2$ The foci are at $(0,\pm 6\sqrt 2)$.