Consider the paraboloid z = x^2 + y^2. The plane 8 x - 6 y + z - 9 = 0 cuts the paraboloid, its intersection being a curve.
Find "the natural" parametrization of this curve.
Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your starting point, give the parametrization of the curve on the surface.