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Homework Help: Ruled surfaces help

  1. May 28, 2015 #1
    Hello, I am studying for an analytic geometry final but I am totally lost for this problem... We didn't even cover this topic in class (my prof didn't show up for class for two weeks) and I have no clue on how to do it. If anyone could help I would appreciate it.

    Question: Prove that the equation: $$x^2-y^2+xy-1=0$$ is a ruled surface.

    I understand that a ruled surface is a surface composed of straight lines but that is as far as my knowledge goes for this question... Again any help is appreciated.
  2. jcsd
  3. May 28, 2015 #2


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    You're close, but this article gives a more complete definition of ruled surfaces:

  4. May 28, 2015 #3


    Staff: Mentor

    Unrelated to your question -- the homework template is required. If you post a question again, please don't delete the three parts.
  5. May 28, 2015 #4


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    With the ##z## variable missing, isn't this a cylindrical surface? For any fixed ##(x,y)## satisfying the equation, what happens to ##(x,y,z)## as you vary ##z##?
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