Cable Vertex
Conic Sections parabolic shape application?
I have been trying to figure this out with no luck. Can someone please help me?
Suspension bridge:
Each cable of the Golden Gate Bridge is suspended (in parabola shape) between 2 towers that are 1280 meters apart. The top of each tower is 152 meters above the roadway . The cables touch the roadway at the midpoint between the towers. Write an equation for the parabolic shape of each cable.
*The diagram shows the cables connect at the vertex. The two points are (-640,152) and (640,152).
The parabola has a vertical axis, and vertex (0, 0).
Its equation is therefore:
x^2 = ky
When x = +/- 640, y = 152
Substituting these values:
640^2 = 152k
k = 152 / 640^2
The equation is:
x^2 = (152 / 640^2) y
or approximately:
x^2 = 3.71 * 10^(-4) y.
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