Question

Rewrite in Polar Form....
x^(2)+y^(2)-6y-8=0

Answer 1

r^2=6rsin(theta)+8

Explanation:

I took the quiz <3

Answer 2

`\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}`


`\bf 6rsin(\theta)\iff 2\cdot r\cdot \boxed{3\cdot sin(\theta)}\impliedby \textit{so there} \\\\\\ \textit{now, bear in mind we're just borrowing from zero, 0} \\\\ \textit{so if we add, \underline{whatever}, we also have to subtract \underline{whatever}}`


`\bf [r^2-6rsin(\theta)\underline{+[3sin(\theta)]^2}]\quad \underline{-[3sin(\theta)]^2}=8\\\\ \left. \qquad \right.\uparrow \\ \textit{so-called`