Question

How do you convert `x^2 + y^2 = 4x + 4y` to polar form?

Answer 1

`r=4costheta+4sintheta`

Explanation:

`x=rcostheta`
`y=rsintheta`
`LHS=x^2+y^2=r^2cos^2theta+r^2sin^2theta=r^2(cos^2theta+sin^2theta)=r^2`
As `cos^2theta+sin^2theta=1`
`RHS=4rcostheta+4rsintheta=4r(cos theta+sintheta)`
LHS=RHS
`r^2=4r(costheta+sintheta)`
Finally `r=4(costheta+sintheta)`