In a suspension bridge, the shape of the suspension cables is parabolic. The bridge shown in the fogure has towers that are 400m apart, and the lowest point of the suspension cables is 100m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the lowest point of the cable.
a. y^2 = 1,600 x
b. x^2 = -400 y
c. x^2 = 400y
d. x^2 = 800 y
e. x^2 = 1,600 y
+23254 Since the origin is placed at the lowest point of the cable, its coordinates are (0,0).
Since this point is 100 m below the top of the towers and the distance from this point to each tower is 200 m, the coordinates of the tops of the towers are (-200, 100) and (200, 100).
A parabola opening upward has the equation: x2 = ay.
For the point: (200, 100) ---> 2002 = a·100 ---> a = 400 ---> x2 = 400y.
[Also: it is true that a hanging cable has the shape of a catenary, that shaped is changed into a parabola when weights are attached.]
