Natural parametrization or a curve

[eva_92]

Hello,
I need the natural parametrization or a curve contained in the surface z=x^2+y^2, that goes through the origin, expressed as a function of the arc length, i.e., I need r(s)=r(x(s),y(s)).
Thank you very much!
Eva

 

[eva_92]

I forgot to say: with x(s=0)=0, y(s=0)=0, dx/ds (s=0)=cos(a) and dy/ds(s=0)=sin(a), win a constant