Question

Consider the paraboloid $z = x^2 + y^2$. The plane $2x - 5y + z - 5 = 0$ 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. $c(t) = (x(t), y(t), z(t))$, where $x(t) = $ $y(t) = $ $z(t) = $

          Consider the paraboloid $z = x^2 + y^2$. The plane $2x - 5y + z - 5 = 0$ 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.
$c(t) = (x(t), y(t), z(t))$, where
$x(t) = $
$y(t) = $
$z(t) = $

consider the paraboloid z x2 y2 the plane 2x 5y z 5 0 cuts the paraboloid its intersection being a curve find the natural parametrization of this curve hint the curve which is cut lies above 61193

Added by Tamara V.

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