Question

How do you graph the polar equation `r^2=9sin2theta`?

Answer 1

`(x^2+y^2)^2-18xy=0`

Explanation:

`x=rhocostheta` from which `costheta=x/rho`
`y=rhosintheta` from which `sintheta=y/rho`
`rho=root2(x^2+y^2)`
`rho^2=x^2+y^2`
`rho^2=18sinthetacostheta=`
`rho^2=18(xy)/rho^2`
`rho^4=18xy`
`(x^2+y^2)^2=18xy`