Answer
$y^2 - \dfrac{x^2}{4} = 4 $
Work Step by Step
$x = 4 \cot{t} \hspace{30pt} y = 2 \csc{t} $
$x^2 = 16 \cot^2{t} \hspace{30pt} y^2 = 4 \csc^2 {t}$
$4y^2 = 16 \csc^2{t}$
$4y^2 = 16+16 \cot^2 {t}$
$4y^2 = 16+x^2$
$y^2 - \dfrac{x^2}{4} = 4 $
