Two Pieces of a Fence (AR Modeling Challenge)

Using only 2 surface equations (with domain restrictions), how can we reconstruct what is seen in the screencast below? Clues: 1) The vertex of the blue paraboloid of revolution is (3, 0, 5). 2) The point lies on the paraboloid of revolution. 3) The radius of the circular opening at the bottom of the paraboloid of revolution = . 4) The pink surface is half a cylinder. This cylinder has a radius = 2. 5) The axis of the cylinder is can be found by translating the xAxis by the vector <0, 0, -2>.

Quick Demo