Calculus 3

Consider the paraboloid z = x- +y . The plane 5x - 9y +z-3 =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 parametrization 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. c(t ) = (x(t), y(t), z(t) ), where x (t ) = y (t ) = :(t)