Answer
$$\eqalign{
& x = {y^2} \cr
& {\text{The resulting curve is a parabola that opens to the right}} \cr} $$
Work Step by Step
$$\eqalign{
& r = \cot \theta \csc \theta \cr
& {\text{Use the quotient identities }}\cot \theta = \frac{{\cos \theta }}{{\sin \theta }}{\text{ and csc}}\theta = \frac{1}{{\sin \theta }} \cr
& r = \left( {\frac{{\cos \theta }}{{\sin \theta }}} \right)\left( {\frac{1}{{\sin \theta }}} \right) \cr
& r = \frac{{\cos \theta }}{{{{\sin }^2}\theta }} \cr
& r{\sin ^2}\theta = \cos \theta \cr
& {\text{Multiply both sides of the equaqion by }}r \cr
& {r^2}{\sin ^2}\theta = r\cos \theta \cr
& {\left( {r\sin \theta } \right)^2} = r\cos \theta \cr
& {\text{Where }}x = r\cos \theta {\text{ and }}y = r\sin \theta .{\text{ Then}} \cr
& {\left( y \right)^2} = x \cr
& x = {y^2} \cr
& {\text{The resulting curve is a parabola that opens to the right}} \cr} $$
