Answer
$4x^2+y^2+z^2=16$
Work Step by Step
We can rewrite as: $4x^2+y^2=16$
$\implies \dfrac{x^2}{4}+\dfrac{y^2}{16}=1$
$\implies x=(y^2-2y)+(z^2-4z)+5$
We see that the ellipse is rotated around the x-axis and traces are parallel to the yz plane.
Now, $\dfrac{x^2}{4}+\dfrac{y^2}{16}+\dfrac{z^2}{16}=1$
This implies that $4x^2+y^2+z^2=16$
