Consider the paraboloid z = ²+². The plane 6x Find "the natural" parametrization of this curve. 6y+-3-0 cuts the parabol

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Consider The Paraboloid Z The Plane 6x Find The Natural Parametrization Of This Curve 6y 3 0 Cuts The Parabol 1 (19.66 KiB) Viewed 75 times

Consider the paraboloid z = ²+². The plane 6x Find "the natural" parametrization of this curve. 6y+-3-0 cuts the paraboloid, its intersection being a 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. c(t) = (z(t), y(t), z(t)), where x(t) y(t)