Consider the paraboloid z = x^2 + y^2. The plane 2x - 5y + z - 8 = 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 parametrization starts at the point on the circle with the largest x coordinate. Using that as your starting point, give the parametrization of the curve on the surface.
c(t) = (x(t), y(t), z(t)), where
x(t) =
y(t) =
z(t) =