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Let $S$ be the piece of the cylinder $x^2 + z^2 = 1$ which is to the right of the $xz$–plane and to the left of the plane $y = 1 + x$.

Find the equation of the tangent plane to $S$ at the point $( \frac{1}{\sqrt{2}}, 1, \frac{1}{\sqrt{2}})$

Currently doing practice questions from old midterms and I dont know how to solve this problem. I understand how one would go about finding the equation of the tangent plane, but how do make the parametric equation given that you know the cylinder is bounded by $y = 1 + x$ and $y = 0$

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    What does "to the right" mean? – 2017-02-27
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    there was a diagram that came with this question and a bound which is y=0 – 2017-02-27
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    The two planes intersecting the cylinder have no effect on the tangent plane to that given point. Since you say it's an exam problem, perhaps those planes are needed for another part. – 2017-02-27
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    yes there is a part b to the question Find the surface area of S. I just dont understand how to create a parametric equation given these equations. – 2017-02-27
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    You only need the equation for the cylinder since that is the surface that the given point is on. (tangent planes are local!) – 2017-02-27

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