Chapter 9 Quadratic Relations and Conic Sections - 9.6 Translate and Classify Conic Sections - 9.6 Exercises - Skill Practice - Page 655: 17

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The standard form for the ellipse is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ We find $h=1\\k=4$ Distance from the center to a vertex: $a=5-h=5-1=4$ Distance from the center to a focus is: $c=3-h=3-1=2$ Find $c^2=a^2-b^2\\2^2=4^2-b^2\\b^2=16-4=12$ We have an equation: $\frac{(x-1)^2}{16}+\frac{(y-4)^2}{12}=1$