The length of an implicit curve Problem 10 Find the length of the curve, given by the equations F1(x,y,z)=x4+y2/2+z2=12F2(x,y,z)=x2+y2−4z2=8. \begin{aligned} F_1(x,y,z)&=x^4+y^2/2+z^2=12\\ F_2(x,y,z)&=x^2+y^2-4z^2=8. \end{aligned} F1(x,y,z)F2(x,y,z)=x4+y2/2+z2=12=x2+y2−4z2=8.