The suspension cables of a bridge

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Question from Mike, a student:

what is the formula for the suspension cables of a bridge.
The towers are 200 ft above the roadway
The towers are 3400 ft apart
The cable if at 8ft in the middle of the span

Mike,

In reality this problem is very difficult, as it depends on the relative weights of the curved cables and roadway. If the cables had all the weight, the curve would be a catenary (y = cosh x). If all the weight is in the roadway, it would be a parabola (y = x²). "College algebra" texts frequently pretend the latter is the case. (You are expected to understand this convention!)

So, if (0,0) is taken to be the center of the roadway, under the lowest point and on the line of symmetry, the cables are assumed to follow the curve y = c + ax².

What is c? (y = 8 when x = 0)
What is a? (y = 200 when x = 1700)

Good Hunting!
RD

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.