r2=x2+y2
and
sin(θ)=y/r
Therefore,
r=SQRT(x2+y2)
and
6sin(θ)=6yr
The original equation turns into:
SQRT(x2+y2)=6y/r
or
x2+y2=6y
Completing the square turns this into
x2+(y−3)^2=9
, a circle centered at
(0,3) with a radius of 3
The area of that circle is 9π
