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Hyperbola Arch

  1. Feb 5, 2013 #1
    1. The problem statement, all variables and given/known data
    An arch is the shape of a hyperbola. IF it s 300m wide at its base and has a maximum height of 100m, how high is the arch 30m from the end ?

    Note: this is a rectangular hyperbola.
    2. Relevant equations

    (y-h)^2 - x^2 = a

    3. The attempt at a solution

    I determined the verticies is (0,0) and there are two points (-150,-100), (150,100) I also know that there must be a vertical translation for the centre to be higher than (0,0).

    But what I can figure out is how to solve for h and a using two different coordinates. If someone could help me with the algebra that'd be awesome.
     
  2. jcsd
  3. Feb 5, 2013 #2

    haruspex

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    How do you get (-150,-100)? That would be underground, no? What about y when x = 300?
     
  4. Feb 6, 2013 #3
    I'm trying to set it as easily as I can without a horizontal shift. However maybe a vertice of (0,100) and points (-150,0) and (150,0) would be better.
     
  5. Feb 6, 2013 #4

    haruspex

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    Either way is fine, but I think you had the coordinates wrong in your first way. It looked like you had the origin on the ground at one end of the arch, right? So the y coord should never have been negative.
    The set you propose now, with the arch endpoints symmetric about the origin, looks right. So, what equations do you get?
     
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