The projection of the cylinder on the Oxy-plane is a circle , which has this parametric equation

Also

So,

See the plot, where

- the blue line is

- the red line is

For Maple

with(plots):

A := spacecurve([cos(t), sin(t), sqrt(1-cos(t)^2)], t = 0..2*Pi, color=red, thickness=3):

B := spacecurve([cos(t), sin(t), -sqrt(1-cos(t)^2)], t = 0..2*Pi, color=blue, thickness=3):

display(A, B, axes=normal, scaling=constrained, view=[-2..2, -2..2, -2..2], numpoints=1000);