Circular path of a point on a paraboloid (improved)

Ideas
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1

A point P moves over the paraboloid z = x^2 + y^2 so that its projection to the plane XY runs through the circumference x^2 + y^2 = x, z = 0, at a constant angular velocity inrad/sec. Parameterize the trajectory of P as a function of time. Deduce that it is a flat curve and calculate its Frenet trihedron, its curvature and its torsion in each P. Obtain the normal and tangential acceleration of P at every moment.

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