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Math Help - Fitting a hyperbola to data

  1. #1
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    Deducing formula for hyperbola from asymptotes

    Hi!

    I have some data which I want to fit a hyperbola to, but i do not know how to?!?!

    My exact question would be: If i know the asymptotes, can i construct a hyperbola which fits?

    I am using cartesian coordinates, and switching to another system is out of the question.

    Below is picture illustrating the data:
    Fitting a hyperbola to data-tempendata3.png

    Thnx
    Last edited by henxan; February 8th 2010 at 12:36 AM. Reason: The title was not descriptive enough
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  2. #2
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    It is best to use a computer for this many data points, do you have any software packages? ms excel should do the job.
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  3. #3
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    Problem not so much "fitting" as "finding form of formula"

    Quote Originally Posted by pickslides View Post
    It is best to use a computer for this many data points, do you have any software packages? ms excel should do the job.
    Thnx for the reply. .. The problem is not fitting the data, it's figuring out a hyperbola which follows the asymptotes.

    The program I intend to use is GNUplot, which seem to work fine. My problem is finding a hyperbola which has the form of:

    a*x+b when x->-infinity
    C when x-> +infinity

    So what i really need to know is a cartesian method of deducing the formula for a hyperbola based on the asymptotes
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  4. #4
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    Quote Originally Posted by henxan View Post
    The program I intend to use is GNUplot, which seem to work fine. My problem is finding a hyperbola which has the form of:
    I'm sorry I don't know this program, i'm sure there would be an option that gives you the equation you are looking for.


    Quote Originally Posted by henxan View Post
    Thnx for the reply. .. The problem is not fitting the data, it's figuring out a hyperbola which follows the asymptotes.
    Once it has given you the equation it will probably be in the form

    y=\frac{a}{x-b}+c where b is the vertical and c is the horizontal asymptotes.
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  5. #5
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    Well, the problem is that the vertical asymptote of the hyperbola is not vertical but diagonal ..

    I have tried searchin all over the interwebz, but nothing helpful. GNUplot only takes functions for trendlines, retrofitting them to the data. Other programs, at least Excel, is absolutely useless in suggesting trends for the data.
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  6. #6
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    Quote Originally Posted by henxan View Post
    I have some data which I want to fit a hyperbola to, but i do not know how to?!?!

    My exact question would be: If i know the asymptotes, can i construct a hyperbola which fits?
    If the sloping asymptote has equation ax + by + c = 0, and the other asymptote is the horizontal line y = d, then the equation of the hyperbola will be (y-d)(ax + by + c) = k, for some constant k.
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  7. #7
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    The SOLUTION!!! :D

    Quote Originally Posted by Opalg View Post
    If the sloping asymptote has equation ax + by + c = 0, and the other asymptote is the horizontal line y = d, then the equation of the hyperbola will be (y-d)(ax + by + c) = k, for some constant k.
    Hi, and thanks for the reply!

    I actually discovered the solution myself yesterday. Firstly I happend on the webpage http://cs.jsu.edu/~leathrum/Mathlets/conics.html ... I then fiddled around with the constants and discovered something like this:

    2xy+y^2-F=0 (ERROR CORRECTED: y->y^2)

    Solving this for y gave me

    y=sqrt(x^2-F)-x

    taking consideration to x and y offset, plus scaling gave me:
    y=(sqrt((b-x)^2-c) - x)*a+d

    OR, the correct expression in GNUplot:
    f(x)=(a*(sqrt((b-x)**"+c)-x)+d)

    Where
    a): vertical scaling
    b): x-offset
    c): constant connected to the focal point (curving)
    d): y-offset

    Then I solved this out in GNUplot

    fit [x=minimum_x_value:max_x_value] f(x) "tempendata.dat"(my datafile) via a,b,c,d

    And this is what came out:
    Fitting a hyperbola to data-test00test.png

    I seem pretty satisfied now
    Last edited by henxan; February 9th 2010 at 01:54 AM. Reason: error in formula
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