![\bf x^2+y^2-6y-8=0\qquad \begin{cases} x^2+y^2=r^2\\\\ y=rsin(\theta) \end{cases}\implies r^2-6rsin(\theta)=8 \\\\\\ \textit{now, we do some grouping}\implies [r^2-6rsin(\theta)]=8 \\\\\\\ [r^2-6rsin(\theta)+\boxed{?}^2]=8\impliedby \begin{array}{llll} \textit{so we need a value there to make}\\ \textit{a perfect square trinomial} \end{array}](/tpl/images/0208/7812/240ff.png)
![\bf [r^2-6rsin(\theta)\underline{+[3sin(\theta)]^2}]\quad \underline{-[3sin(\theta)]^2}=8\\\\ \left. \qquad \right.\uparrow \\ \textit{so-called "completing the square"} \\\\\\\ [r-3sin(\theta)]^2=8+[3sin(\theta)]^2\implies [r-3sin(\theta)]^2=8+9sin^2(\theta) \\\\\\ r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}\implies r=\sqrt{8+9sin^2(\theta)}+3sin(\theta)](/tpl/images/0208/7812/04f18.png)
Rewrite in polar
x^(2)+y^(2)-6y-8=0...
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