Answer
$$\dfrac{\tan 2-2}{2 \tan 2 +1}$$
Work Step by Step
We have: $\dfrac{dr}{ d \theta}=\dfrac{-1}{4}$
$\dfrac{dy}{dx}=\dfrac{dy/d \theta }{dx/d \theta }\\=\dfrac{r \cos \theta+\sin\theta \dfrac{dr}{ d \theta}}{- r \sin \theta+\cos\theta \dfrac{dr}{ d \theta}}$
Now,
$\dfrac{dy}{dx}=\dfrac{1- (\dfrac{1}{2}) \tan 2}{-\tan 2-\dfrac{1}{2}}\\=\dfrac{\tan 2-2}{2 \tan 2 +1}$
