1. The problem statement, all variables and given/known data. Parametrize a circumference contained in the plane [itex]x+y+z=1[/itex], centered at [itex](2,-2,1)[/itex], and of radius [itex]40[/itex]. 2. The attempt at a solution. At first I thought I could intersect the plane [itex]x+y+z=1[/itex] with the sphere [itex](x-2)^2+(y+2)^2+(z-1)^2=40^2[/itex], but then I realized that this is wrong: the circumference can be obtained intersecting the given plane with some sphere, but this sphere doesn't necessarily have a radius of [itex]40[/itex]. So, what can I do know? Could I describe the circumference using polar coordinates? I had in mind a parametrization of the form: [itex]σ(t)=(40cos(t)+2, 40sin(t)-2, 1)[/itex] [itex]0≤t≤2π[/itex] but I'm not sure if this circumference lies on the plane.