Consider the paraboloid \( z=x^{2}+y^{2} \). The plane \( 8 x-9 y+z-3=0 \) cuts the paraboloid, its intersection bein a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the \( x y- \) 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 \( x(t)= \) \( y(t)= \) \( z(t)= \) submit answer
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