anonymous
  • anonymous
For each of the following equtions describe the surface and identify the traces. What does it mean by traces? x^2+y^2-2z=0 Thank you very much for your help!!!
Precalculus
katieb
  • katieb
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anonymous
  • anonymous
means the set of all points that fit this equation http://www.wolframalpha.com/input/?i=x^2%2By^2-2z%3D0
anonymous
  • anonymous
oooh "traces" my fault
anonymous
  • anonymous
cross section parallel to a plane \(xy\) trace, set \(z=0\) for example

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anonymous
  • anonymous
so in this case the \(xy\) trace is given by the equation \(x^2+y^2=0\) which is a point at the origin of the \(xy\) plane
anonymous
  • anonymous
and the \(xz\) trace is \(x^2-2z=0\) or \(x^2=2z\) a parabola
anonymous
  • anonymous
Ok, I understand. Thank you!

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