Answer
$${\text{The equation represents a circle with radius }}r = 3$$
Work Step by Step
$$\eqalign{
& r = 6\sin \theta \cr
& {\text{Multiply both sides of the equation by }}r \cr
& {r^2} = 6r\sin \theta \cr
& {\text{Convert to rectangular form, using }}y = r\sin \theta ,{\text{ }}{r^2} = {x^2} + {y^2} \cr
& {x^2} + {y^2} = 6y \cr
& {x^2} + {y^2} - 6y = 0 \cr
& {\text{Completing the square}} \cr
& {x^2} + {y^2} - 6y + 9 = 9 \cr
& {x^2} + {\left( {y - 3} \right)^2} = {\left( 3 \right)^2} \cr
& {\left( {x - h} \right)^2} + {\left( {y - k} \right)^2} = {r^2} \cr
& {\text{The equation represents a circle with radius }}r = 3 \cr
& {\text{centered at }}\left( {0,3} \right) \cr
& {\text{Graph}} \cr} $$
