Mathematical Model of a Catenary

Hi everyone,

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)

0

39.1

78.2

117.3

156.4

195.5

234.6

273.7

312.8

351.9

391

430.1

469.2

Y Axis (cm)

90

68.5

51

37.2

27.4

19.7

17.8

19.7

27.4

37.2

51

68.5

90

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,

Daniel