# How to find the projection of a cylinder projected onto a plane?

Say you are given the equations:

$x + y + z = 6$ and $x^2 + y^2 = 1$

You can easily find the plane and cylinder accordingly. But how do you find the projection of the cylinder onto that plane. The $x$ boundaries should be the radius of the circle.

I've been told you parametrise both equations and work from there, is that correct?

This is for evaluating Stokes' Theorem by the way.

• Are you sure that you mean "projection"? The projection of the cylinder onto the plane is like the shadow of the cylinder. Do you mean intersection? – Kyle Jun 9 '14 at 13:25
• @Dan Do you mean projection of (the ellipse) intersection ( between cylinder and and plane) onto a coordinate plane? – Narasimham Nov 1 '18 at 6:12

$x = \cos t, \,y = \sin t, \, z = 6-\cos t-\sin t;\, t\, \epsilon \, \langle 0,2\pi\rangle$