It is best to use a computer for this many data points, do you have any software packages? ms excel should do the job.
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:
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
where b is the vertical and c is the horizontal asymptotes.
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.
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
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:
a): vertical scaling
c): constant connected to the focal point (curving)
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:
I seem pretty satisfied now