This past weekend I installed a new bi-fold door on a closet in the attic. The door consists of two panels, each one foot wide, hinged together in the middle. One side of one panel is fixed to the wall, while the other side of the other panel runs along track along the top of the door. As the door opens and closes, it rubs against a carpet on the attic floor, tracing out a path on the carpet pile.

What is the equation of the path traced out by the door on the carpet?

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