Hi I don't understand how you can take a cylinder with equation x2+y2=2x And rewrite it to (x-1)2+y2=1 And then it suddenly becomes the equation for the base circle of the cylinder. Would it not usually require that you remove some variable to transform it from 3D to 2-dimensional? If we have a paraboloid z=1-x2+y2 you can insert the plane z=0 and get the circle 1=x2+y2 which makes sense because you remove a variable. How does this cylinder example work? I'd love to understand it more clearly.