We will have the following:
First, we remember that:
[tex]\begin{cases}x=r\cos (\theta \\ \\ y=r\sin (\theta)\end{cases}[/tex]
So:
[tex]x^2+y^2-10y=0\Rightarrow(r\cos (\theta))^2+(r\sin (\theta))^2-10(r\sin (\theta))=0[/tex][tex]\Rightarrow r^2\sin ^2(\theta)+r^2\cos ^2(\theta)-10r\sin (\theta)=0\Rightarrow r^2(\sin ^2(\theta)+\cos ^2(\theta))-10r\sin (\theta)=0[/tex][tex]\Rightarrow r^2(1)-10r\sin (\theta)=0\Rightarrow r(r-10\sin (\theta))=0[/tex][tex]\Rightarrow r-10\sin (\theta)\Rightarrow r=10\sin (\theta)[/tex]
