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Homework Help: Hyperbolic Geometry Question

  1. Oct 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove that the magnitude of the impact parameter B equals the length (-b) of the hyperbolic semiminor axis.

    2. Relevant equations

    |B|=|b|=|a|sqrt(e^2-1)


    3. The attempt at a solution

    I really don't know where to start. I was thinking of finding a relation between a and b but that is just the right hand side of the equation above (for hyperbolic geometry). I was thinking about the Pythagorean theorem, but then I don't know how |B|=|a+b| would become |a|sqrt(e^2-1). Could anyone help me along the right direction? Thanks.
     
  2. jcsd
  3. Oct 6, 2008 #2
  4. Oct 7, 2008 #3
    bumping one more time, is there anyone out there that can help?
     
  5. Oct 7, 2008 #4

    Dick

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    Science Advisor
    Homework Helper

    I would do it this way. Take a general hyperbola in standard position. x^2/a^2-y^2/b^2=1. That puts a vertex at the point xy point (sqrt(a^2+b^2),0). An asymptote is the line y=bx/a. The impact parameter is the distance from the vertex to the asymptote line. If you work that out you should get b. Which is the semi-major axis.
     
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