Question

What is the polar form of equation `x^2+(y-3)^2=9`?

Answer 1

`r=6sintheta`

Explanation:

The relation between polar coordinates `(r,theta)` and Cartesian coordinates `(x,y)` is given by `x=rcostheta` and `y=rsintheta` which gives us `x^2+y^2=r^2`. Hence,

`x^2+(y-3)^2=9` can be written as

`x^2+y^2-6y+9=9`

or `r^2-6rsintheta=0`

and dividing by `r`, we get

`r-6sintheta=0`

or `r=6sintheta`