Polar coordinates to rectangular

Question

I was asked to convert $r=\frac4{\cos \theta -4 \sin \theta}$ to rectangular coordinates.

So far, I know that $x=r\cos\theta$ and $y=r \sin \theta$.

I multiplied both sides by $r$ to get $r^2 = \frac4{r\cos \theta -4 r\sin \theta}$

I want to assume that because of what I know, that $r^2 = \frac4{x-4y}$.

Maybe I can square root both sides to get the final answer - or did I make a mistake?

Answer 1

HINT

$$r=\frac4{\cos \theta -4 \sin \theta}\implies r\cos \theta-4r \sin \theta=4$$