On page 80 of Spivak's Calculus, 4th Edition, he writes:
One of the simplest subsets of this three-dimensional space is the (infinite) cone illustrated in Figure 2; this cone may be produced by rotating a "generating line," of slope $C$ say, around the third axis. (Here is a link to the Figure 2)
For any given first two coordinates $x$ and $y$, the point $(x,y,0)$ in the horizontal plane has distance $\sqrt{x^{2} + y^{2}}$ from the origin, and thus
(1) $(x,y,z)$ is on the cone if and only if $z=\pm C \sqrt{x^2+y^2}$
I don't understand how (1) follows from the preceding paragraph. Can someone please shed some light on this? Thank you in advance for any help provided.