Question

Consider the paraboloid z = x^2 + y^2. The plane 8x - 5y + 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 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) = (x(t), y(t), z(t)), where x(t) = y(t) = z(t) =

          Consider the paraboloid z = x^2 + y^2. The plane 8x - 5y + 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 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) = (x(t), y(t), z(t)), where x(t) = y(t) = z(t) =

Consider the paraboloid z = x^2 + y^2. The plane 8x - 5y + 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 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) = (x(t), y(t), z(t)), where x(t) = y(t) = z(t) =

Added by Kevin K.

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