Consider the paraboloid z=x2+y2. the plane 8x−5y+z−2=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 parameterization 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( wherex(t)=y(t)=z(t)=