Basically, what we need to do here is to convert all the \(x\)’s and \(y\)’s into \(r\)’s and \(\theta \)’s using the following formulas.

\[x = r\cos \theta \hspace{0.25in}\hspace{0.25in}y = r\sin \theta \hspace{0.25in}\hspace{0.25in}{r^2} = {x^2} + {y^2}\]

Don’t forget about the last one! If it is possible to use this formula (and you can see where we’ll use it in the case can’t you?) it will save a lot of work!

First let’s substitute in the equations as needed.

\[\frac{{4\left( {r\cos \theta } \right)}}{{3{r^2}}} = 6 - \left( {r\cos \theta } \right)\left( {r\sin \theta } \right)\]

Finally, as we need to do is take care of little simplification to get,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{4\cos \theta }}{{3r}} = 6 - {r^2}\cos \theta \sin \theta }}\]