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HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal vect

  1. Jul 12, 2011 #1
    Consider the hyperbola y^2-x^2=1 (y>0)
    a.) Find a parameterization for the curve and write it in vector form, R(t)
    (b) Calculate the unit tangent vector as a function of the parameter.
    (c) Calculate the unit normal vector and the curvature vector as a function of the parameter.
     
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  3. Jul 12, 2011 #2

    micromass

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    Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

    What did you try already??

    You must find function f and g such that

    [tex]f(t)^2-g(t)^2=1[/tex]
     
  4. Jul 12, 2011 #3
    Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

    I tried to set x=t and y= sqrrt(1+t^2) ...it comes out nasty and ugly, so ugly that i didn't even finish it..i'm not sure if there's a better way to do it.
     
  5. Jul 12, 2011 #4
    Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

    soccer*star, is this problem due tomorrow by any chance?
     
  6. Jul 13, 2011 #5

    micromass

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    Re: HELP! i'm trying to parametrize a hyperbola to find it's unit tangent and normal

    If you would have [itex]x^2+y^2=1[/itex], then there's an easy choice:

    [tex]\sin^2(t)+\cos^2(t)=1[/tex]

    But now you have [itex]x^2-y^2=1[/itex]. Can you do something similar?
     
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