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How to determine b in a conic hyperboal graph

  1. Dec 10, 2009 #1
    How to determine "b" in a conic hyperboal graph

    1. The problem statement, all variables and given/known data

    http://img143.imageshack.us/img143/3391/91667159.jpg [Broken]
    (x-1)2/22 - y2/b2 =1
    I can't find any good point for me to solve b..I don't know what to do..
    Is there any way to solve b without using the point?
    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 10, 2009 #2

    Dick

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    Re: How to determine "b" in a conic hyperboal graph

    Not really. You need a point off the x-axis to solve for b. It looks like it passes near the point (4,1). That will let you get an approximate value for b.
     
  4. Dec 11, 2009 #3
    Re: How to determine "b" in a conic hyperboal graph

    I see, thanks!
     
  5. Dec 11, 2009 #4

    HallsofIvy

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    Re: How to determine "b" in a conic hyperboal graph

    What you really need, in order to find b, is the equation of asymptotes. If a hyperbola has equation
    [tex]\frac{(x-x_0)^2}{a^2} - \frac{(y-y_0)^}{b^}= 1[/tex]
    then its asymptotes are [itex]y-y_0= \pm b(x-x_0)/a[/itex]

    On this graph, it looks to me like an asymptote passes through (1,0) and (3,1) so has equation y= (1/2)(x- 1). That gives you a slightly different answer than assuming the graph passes through (4,1) but Dick and I are both "eyeballing" the graph.
     
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