Why 2 equations of the form F(x,y,z) = 0 for one 3D curve

Question

It says in my analysis 2 book that a curve is given by $F_1(x,y,z) = 0$ and $F_2(x,y,z) = 0$. Why do we need two equations of $x,y,z$ To define a curve in 3D, shouldn't one be enough?

Answer 1

HINT

One equation gives you a surface : $$x^2+y^2+z^2-2=0 \tag{1}$$

is a sphere

Imagine another surface intersecting this sphere, for example, a plane : $$z +2=0\tag{2}$$

Solving both gives you a circle :