Question

How do you convert `4=(x-4)^2+(y-5)^2` into polar form?

Answer 1

`r^2-8rcostheta-10rsintheta+37=0`

Explanation:

Relation between polar coordinates `(r,theta)` and rectangular coordinates is given by `x=rcostheta`, `y=rsintheta`, `r^2=x^2+y^2` and `tantheta=y/x`.

Hence `4=(x-4)^2+(y-5)^2` can be written as

`x^2-8x+16+y^2-10y+25=4` or

`x^2+y^2-8x-10y+37=0` or

`r^2-8rcostheta-10rsintheta+37=0`