Why does a suspension bridge use a parabola?

The actual wire concerning the actual systems is proved to be a parabola. I don't want to realize how to mathematically show it's really a parabola as well. I just want to learn wherefore set it up having a parabola? Have you thought to an electric arc as well as catenary? If it has been, order the catenary rather than parabola, might it's balance be different?

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"If you calculate the load on a suspension bridge and its distribution, the Shear force and Bending moment diagrams will yield equations for design.... these equations in case of a suspension bridge have degree=2... therefore it becomes a second degree curve, i.e. Parabola...( for. eg. y = k.x^2) A catenary is not a second degree curve... it is an exponential one and hence cannot be used."

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In a suspension bridge, the roadway is actually hanging from large cables.

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