Question

How do you convert `-xy=x+4y^2` into a polar equation?

Answer 1

`4r^2sin^2theta+r^2costhetasintheta+rcostheta=0`

Explanation:

`-xy=x+4y^2`

Use equations `x=rcos theta,y=rsin theta`

`-rcos theta xx rsintheta=rcos theta+4r^2sin^2theta`

`-r^2costhetasintheta=rcostheta+4r^2sin^2theta`

`0=4r^2sin^2theta+r^2costhetasintheta+rcostheta`