Showing a curve is in a surface

Question

Given the following curve $$\alpha(t)=(4sin(t),t,-4cos(t))$$ I gotta show it's in a surface.

I know $$x^2(t)+y^{2}(t)+z^{2}(t)=16+t^{2}$$ but I'm not sure what can I do with it.

Answer 1

It is a helix, clearly situated on the cylindrical surface with equation:

$$x^2+z^2=16$$