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May 28, 2015

Homework Help: Math

Posted by Derek A on Sunday, February 7, 2010 at 11:02pm.

Consider the paraboloid z=x^2+y^2. The plane 3x-2y+z-7=0 cuts the paraboloid, its intersection being a curve.
What is the "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.

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