Answer
$$r=\frac{cot \theta}{4 sin\theta}$$
Work Step by Step
Given: $$4y^{2} = x$$
Rewtite the given equations as: $$4(rsinθ^{2}) = rcosθ$$
$$4r(sinθ^{2}) = cosθ$$
Thus, $$4r = \frac{cosθ}{sinθ^{2}}$$
or, $$4r = \frac{cotθ}{sinθ}$$
Hence, $$r=\frac{cot \theta}{4 sin\theta}$$
