Consider the paraboloid z=x2+y2. The plane 2x−5y+z−9=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.

Question

Consider the paraboloid z=x2+y2. The plane 2x−5y+z−9=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.

anonymous · Answer

sorry, it copied wrong.  that should be z=x^2+y^2.

anonymous · Answer

and i'm completely stuck.  


c(t)=(x(t),y(t),z(t)), where x(t)=, y(t)= and z(t)=

anonymous · Answer

ur wrong

anonymous · Answer

jk