Let S Be a Circular Cylinder of Radius 0 $( x ( \theta ) , y ( \theta ) , z ( \theta ) )$

Essay

Let S be a circular cylinder of radius 0.2, such that the center of one end is at the origin and the center of the other end is at the point (5, 0, 4).
Let P be the plane containing the base of the cylinder (i.e., the plane through the origin perpendicular to the axis of the cylinder).
In each case, give a parameterization $( x ( \theta ) , y ( \theta ) , z ( \theta ) )$ and specify the range of values your parameters must take on.
(i)the circle in which the cylinder, S, cuts the plane, P.
(ii)the surface of the cylinder S.