# Analytic geometry

A cable of a suspension bridge hangs in the form of a parabola, the supporting towers of the cable being 300 meters apart. The cable passes over the supporting towers at a height of 60 meters above the roadway and the lowest point of the cable is 5 m above the roadway. Find the lengths of the vertical supporting rods from the cable to the roadway at intervals 50 meters from the center of the bridge to a supporting tower.

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1. You have the parabola symmetric to the y-axis

y = ax^2+b
y(0) = 5
y(150) = 60

Now you can find a and b, and thus y(50)

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