# math

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the lions gate bridge in vancuver BC, is a suspension bridge that spans 1516m. Large cables are attached to the tops of the towers, 50m above the road. the road is suspended from the large cables with small vertical cables, the smallest one being 2m. find a quadratic equation to model the large cable shape.

• math -

The cables of a suspension bridge do not follow the path of a parabola, but since that is what the question asks for ...

centre is (2,0), one other point is (758,50)
y = a(x-2)^2 + 0 , using the centre
but (758,50) lies on it
50 = a(756)^2
a = 50/574564

y = 25/287282(x-2)^2

The cables of most suspension bridges form a
"catenary" (from the Latin 'catena' for chain)

the general equation is
y = a/2(e^(x/a) + e^(-x/a))

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