Shape of a suspension bridge One section of a suspension bridge has its weight uniformly d...

Shape of a suspension bridge 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 (see the figure). 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. Suppose coordinate axes are introduced, as shown in the figure.

EXERCISE

(a) Find an equation for the parabola.

(b) Nine equally spaced vertical cables are used to support the bridge (see the figure). Find the total length of these supports.