Hardcore rotation problem in multivariable calculus

[Nikitin]

Homework Statement

Let C be the circle defined by (x-2)²+y² = 1. If this circle is rotated along the y-axis, a torus will form. What is the Cartesian equation for the torus?

The Attempt at a Solution

The solution manual says you just switch the x in (x-2)²+y² = 1 with r=√(x²+z²) and simplify.Why would that work? Why does the x in the first equation equal the radius of the torus? I don't get it.

 

[Nikitin]

help?

 

[tiny-tim]

Hi Nikitin!

if (x,y,z) is on the torus, then so must be (√(x²+z²),y,0)

but that must be on the original circle, so (√(x²+z²) -2)²+y² = 1