How To Mathematically Slice A Parabolic Trough at an Angle?

Asked Nov 05 '13 at 21:39

Active Nov 05 '13 at 21:55

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Given a Parabolic Trough is defined as $y=x^2$ and extending infinitely in the z direction. How may I find the equation of the curve obtained through slicing the parabolic trough using a plane through the x-axis and at an angle $\theta$ from the z-axis?

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edited Nov 05 '13 at 21:55

asked Nov 05 '13 at 21:39

User3910

2,390

You cannot find "the equation" for this curve, if by that you mean a single equation in only $x$, $y$, and $z$. You can find a parameterization of this curve though in terms of some time variable $t$; is that what you seek? – 2'5 9'2 Nov 05 '13 at 21:48
@alex.jordan That is indeed! If there is a way to use complex numbers I would be even more thrilled. – User3910 Nov 05 '13 at 21:58
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$(x,y,z)=(t,t^2,t\cot\theta)$ – Carlos Eugenio Thompson Pinzón Nov 05 '13 at 21:59

How To Mathematically Slice A Parabolic Trough at an Angle?

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