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Let S be the surface defined by the plane $$y+z=2$$ whose sides are the cylinder $$x^2+y^2 = 1$$Find the parameterization of the elliptical surface in cylindrical coordinates. Sorry about the non mathjax equations, but I'm kind of new here and I need some quick help.The problem as it appears on the sheet

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    MathJax is not hard to learn for equations such as these.... why is the help needed quickly, I wonder? – 2017-01-06
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    Doh. Sorry for the edit override. It was not intentional. – 2017-01-06

2 Answers 2

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Hint: the projection of the ellipse on the $XY$-plane is the (bidimensional) disk $x^2 + y^2\le 1$. You can parametrize the disk using polar coordinates. An the equation $y + z = 2$ gives the third coordinate.

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Hint: $$\phi(\theta,z)=(\cos{\theta},\sin{\theta},2-\sin{\theta})$$