Question

one section of a suspension bridge has its weight uniformly distributed between twin towers that are 400 feet apart and rise 90 feet above the horizontal roadway. a cable strung between the tops of the towers has the shape of a parabola, and its center point is 10 feet above the roadway. 1) how do i find the equation of the parabola, and
2) how do I find the total length of the nine equally spaced cables?

Answer 1

make you sketch in such a way that the roadway is the x-axis and the center of the cable is along the y-axis
So the vertex of your parabola is (0,10) and your equation is

y = ax^2 + 10
we know (200,90) must be a point on it, so
90 = a(40000) + 10
a = 80/40000 = (1/500)x^2 + 10

2. length of the nine equally spaced cables?
where does that come from ? no mention of it in your problem

BTW, the cables of suspension bridges do NOT hang in the shape of a parabola. The hang in the shape of a "CATENARY".