Question

Find a parametric representation for the surface. The part of the plane z = x + 3 that lies inside the cylinder x2 + y2 = 9. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of s and/or θ.)

Answer 1

You can use

$x=u\cos v$

$y=u\sin v$

$z=u\cos v+3$

with $0\le u\le3$ and $0\le v\le2\pi$.