Consider the paraboloid $z = x^2 + y^2$. The plane $3 x - 5 y + z - 9 = 0$ 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.

$\mathbf{c}(t) = (x(t), y(t), z(t))$, where
$x(t) =$
$y(t) =$
$z(t) =$