Hyperbolas can be rotated so that the orientation is closer.
You will have to keep modelling until you settle on the Hyperbolic Cosine, , but that's a different animal than those you have suggested.
I have a Yr 11 maths assignment which investigates the geometry of a suspension bridge (mainly catenarys). I used a piece of 5m rope to create the shape of one and recorded the following measurements:
X Axis (cm)039.178.2117.3156.4195.5234.6273.7312.8351.9391430.1469.2
Y Axis (cm)9068.55137.227.419.717.819.727.437.25168.590
One of the questions asks to generate a mathematical model using either y=ax^2, y=ax^3, y=a/x or y = the square root of x.The textbook also states
sometimes non-linear relationships can be reduced to linear relationships. For instance, y =m/x + c is a hyperbola. However, if we substiture p for 1/x, the rule becomes linear: y=mp+c. The graph of y versus p will be the straight line with the gradient of m and the y intercept of c. These values (m and c) can then be established from the graph and thus the hyperbolic model can be determined.
What do I use? How can I generate a model? I have tried but none have worked for more than one value .
Thanks in advance,