A necklace hanging between two fixed points A and B at the same level. The length of the necklace between the two points is 100cm. The midpoint of the necklace is 8cm below Aand B. Assume that the necklace hangs in the form of parabolic curve, find the
equation of the curve.

Question

A necklace hanging between two fixed points A and B at the same level. The length of the necklace between the two points is 100cm. The midpoint of the necklace is 8cm below Aand B. Assume that the necklace hangs in the form of parabolic curve, find the 
equation of the curve.

anonymous · Answer

x^2/50 +y^2/4=1

kropot72 · Answer

The equation that you need is as follows:
$$y=\frac{8}{50^{2}}x ^{2}$$
The derivation is rather complicated, requiring some detailed drawing to enable understanding. My drawing skills are not good enough to help in this respect.
The forces in equilibrium on a part of the necklace are considered. These forces are the tension in the necklace and the weight of the necklace per unit horizontal span.
Note that the final equation does not include the tension in the necklace or weight of the necklace per unit horizontal span.