Find a vector function that parameterizes a curve C which lies in the plane x-y+z=2 and directly above the circle x2 + (y-1)2 = 9
The Attempt at a SolutionSo, in order to parameterize the circle, I simply use x=cos(t), y = sin(t) with some adjustments. Namely, I let x=3cos(t) and y=3sin(t)+1. Then, to determine how the z-coordinates of this curve change according to x,y I use the definition of the plane. So I have z=2-x+y, which I convert using my parametric defintions for x,y.
I have, z=3-3cos(t)+3sin(t). Therefore, my parameterized curve is,