Chapter 9 Quadratic Relations and Conic Sections - 9.7 Solve Quadratic Systems - 9.7 Exercises - Quiz for Lessons 9.6-9.7 - Page 664: 1

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The standard form for an ellipse: $$\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$$ We know $h=3$. Use this to find h: $h=\frac{-10+6}{2}=-2$ Find c: $c=-7-k=-7-(-2)=-6$ Find b by using the formula $a^2+b^2=c^2\\b^2=a^2-c^2\\b^2=8^2-5^2=39\\b=\sqrt 39$ Substitute the values: $$\frac{(x-3)^2}{39}+\frac{(y+2)^2}{64}=1$$