# Replace the polar equations with equivalent Cartesian equations. Then describe o

Replace the polar equations with equivalent Cartesian equations. Then describe or identify the graph. ${r}^{2}=-6r\mathrm{sin}\theta$
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Brighton

${r}^{2}=-6r\mathrm{sin}\theta$
The Cartesian equation is
$⇒{x}^{2}+{y}^{2}+6y=0$
$⇒{x}^{2}+{y}^{2}+6y+9=9$
$⇒{x}^{2}+{\left(y+3\right)}^{2}=9$
$⇒{\left(x-0\right)}^{2}+{\left(y-\left(-3\right)\right)}^{2}={3}^{2}$
Now its the form of of$⇒{\left(x-h\right)}^{2}+{\left(y-k\right)}^{2}={r}^{2}$
Hence it represents a circle with centre at (h,k)(0,-3)& radius 3