we have the equation
rcsc(theta)=8
Remember that
csc(theta)=1/sin(theta)
substitute
r(1/sin(theta))=8
r=8sin(theta)
Multiply both sides by r
r^2=8rsin(theta)
Remember that
y=rsin(theta)
so
r^2=8y
and
x^2+y^2=r^2
therefore
x^2+y^2=8y
Group terms
x^2+(y^2-8y)=0
complete the square
x^2+(y-4)^2=16
