Question

Can someone explain to me why the answer to [write equation using polar coordinates] 3x^2+3y^2=6y is 3r^2- 6rsin(theta)=0 (textbook answer)? Why not r-2sin(theta)=0? Is one more preferred and why?

Answer 1

`3r^2-6r\sin\theta=0` is valid.

`r^2-2r\sin\theta=0` is equally valid.

`r-2\sin\theta=0` is not technically valid because it's possible that
`r=0`, and you can't divide through the above equation by 0. The plots of all three of these options are identical, however.