1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook