Answer
$y=\frac{1}{8}x^2$
See graph
Work Step by Step
1. Use the relation $r\ sin\theta=y, r^2=x^2+y^2$, we have
$r\ sin^2\theta+8sin\theta=r\\ \Longrightarrow r^2\ sin^2\theta+8r\ sin\theta=r^2\\ \Longrightarrow y^2+8y=x^2+y^2$
thus we get $y=\frac{1}{8}x^2$
2. The above parabola with vertex $(0,0)$ (rectangular system) can be shown in the figure.
