Question

How do you find the polar equation for x^2+(y-2)^2-4=0#?

Answer 1

`r=4sintheta`

Explanation:

The relation between polar coordinates `(r,theta)` and rectangular coordinates `(x,y)` are given by `x=rcosthata` and `y=rsintheta` and hence `r=sqrt(x^2+y^2)`

Hence `x^2+(y-2)^2-4=0` can be written as

`x^2+y^2-4y+4-4=0` or using relations between polar and Cartesian coordinates

`x^2+y^2-4y=0`

`r^2-4rsintheta=0` or

`r-4sintheta=0` or `r=4sintheta`