Question

How do you convert `9=(-2x+y)^2-5y+3x` into polar form?

Answer 1

`9=4r^2cos^2(theta)-4r^2sinthetacostheta+r^2sin^2(theta)-5rsintheta+3rcostheta=r(sintheta(r(sintheta−4costheta)−5)+costheta(4rcostheta+3))`

Explanation:

`x=rcostheta`
`y=rsintheta`

`9=(-2(rcostheta)+rsintheta)^2-5rsintheta+3rcostheta`

`9=4r^2cos^2(theta)-4r^2sinthetacostheta+r^2sin^2(theta)-5rsintheta+3rcostheta`

`9=r(sintheta(r(sintheta−4costheta)−5)+costheta(4rcostheta+3))`