The cable of the bridge is parabola. Let the vertex of one of the parabolas be (0, 0), the point at which the cable touches the roadway midway between the towers.

The general form of the parabola is:

x^2 = 4py

We can solve for the equation of this parabola by substituting in the point (200, 50) – the height of one of the towers:

200^2 = 4p*50

p = 200^2/(4*50)

p = 200

Then

x^2 = 4*200y or

x^2 = 800y is the equation for the parabola.

To find the height of the cable 100 meters from a tower, we see that the x-coordinate in our system would be 200 – 100 = 100 m (the distance from the origin out to the cable). Now substitute in 100 m for x into x^2 = 800y to find the height:

100^2 = 800*y

y = 100^2/800

y = 12.5 m

the length of the height of the supporting cable when 100 meters from a tower is 12.5 meters.