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Finding the positive x-value on a hyperbola

  1. Mar 11, 2009 #1
    1. The problem statement, all variables and given/known data
    The curve y^2-3xy+2x^2=4 is a hyperbola with axes rotated from the standard position. Use Newton's Method to find the positive x-value to four decimal places for the point on the hyperbola where y=1.


    2. Relevant equations
    Newton's Method



    3. The attempt at a solution
    I found the first part of Newton's Method by finding the derivative of the equation given, but I don't know how to find f(x) to finish of the formula. I've figured that you can simply plug the y-value into the given equation, make it equal to zero, and then plug it in for f(x), but then I do not know the starting value to use for x. I know how to use Newton's Method and find the derivative, but for this question I just don't know how to find f(x) and the starting x-value needed to solve for the answer. Any help you guys can give would be greatly appreciated, thanks in advance.
     
  2. jcsd
  3. Mar 11, 2009 #2

    lanedance

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    Homework Helper

    hi emethyst

    first substitute y = 1 into your equation and rearrange for

    so it looks like
    f(x) = 0
    and you want to find x that satisfies the equation

    this will be a quadratic so you could in fact solve it, and use the quadratic equation as a check

    then think about a negative parabola (which is what f(x) is...) where would you want to pick a point so that you newton iterations find the positive x value & don't over shoot in the process

    doing an approximate curve sketch might help...
    what is the turning point, and where does the curve intersect f(x) axis when x is zero, should be enough to pick a reasonable point
     
  4. Mar 12, 2009 #3
    Thanks for all the help lanedance, I can say I successfully solved that question now :smile:
     
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