Consider the paraboloid $z=x^2+y^2.$ The plane $6x-9y+z-7=0$ 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 $tso$ that the circle $is$ traversed counterclockwise exactly once $ast$ goes from $0to{2}^{**}pi,$ 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

$x(t)=$

$y(t)=$

$z(t)=$