Answer:
[tex]\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.[/tex]
Step-by-step explanation:
A helix is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides, flattening it out, and noting that a straight line connecting the points becomes helical upon re-wrapping (see attached diagram for helix).
The parametrization for the helix is
[tex]\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.,[/tex]
where [tex]r[/tex] is the radius of the helix, [tex]a[/tex] is the constant, and [tex]t\in [0,2\pi )[/tex] is the parameter
