Chapter 9 Quadratic Relations and Conic Sections - 9.7 Solve Quadratic Systems - 9.7 Exercises - Quiz for Lessons 9.6-9.7 - Page 664: 3

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The standard form for an ellipse: $$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$$ Find the center $(h,k)=(\frac{0+3}{2},\frac{1+1}{2})=(\frac{3}{2},1)$ Find c: $c=6-1.5=4.5$ Find a: $a=3-1.5=1.5$ Find b by using the formula $a^2+b^2=c^2\\b^2=a^2-c^2\\b^2=(4.5)^2-(1.5)^2=18\\b=3\sqrt 2$ Substitute the values: $$\frac{(x-1.5)^2}{2.25}+\frac{(y-1)^2}{18}=1$$