Halogen Lamp (AR Modeling Challenge)
The goal of this GeoGebra Augmented Reality modeling challenge is to author 2 surface equations (with domain restrictions) that model the halogen lamp seen in the screencast below.
Modeling Clues:
1) Both surfaces are parts of 2 different paraboloids of revolution.
2) The blue surface is part of a paraboloid with vertex (0,0,0).
The point lies on the blue surface.
The radius of the bottom circle = 1.
The radius of the top circle = .
3) The pink surface is part of a paraboloid with vertex (0, 0, 0.5).
There is absolutely no overlap between the blue surface and pink surface.