Parametrize a path for the curve that is a circle in the x-y plane that has radius 2 (a) with center (0, 0) going counterclockwise (b) with center (1, 2) going counterclockwise (c) with center (1,2) going clockwise (d) Now modify this to be a path in 3 dimensional space, for a circle "above" the xy plane with a height of z = 3, with center (1,2,3), and moving counterclockwise as we look down from the positive z-axis. Hint: just set z = 3 and compute the other coordinates as in prior examples. (e) Find the formula for a helix that is found on a standard toilet roll interior (hard to come by?): Use centimeters for units. Note that the diameter is 4.2cm, and the height is 11.4cm, and the number of revolutions of the helix is 1 and 1/8th, i.e. 1.125.

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