# Thread: Help finding equations for parabolas

1. ## Help finding equations for parabolas

The shape of a flexible and inelastic cable supporting a load that is uniformly distributed horizontally, like the cables of a suspension bridge, is a parabola.

a) Place the origin of an xy-coordinate system at the lowest point of a parabolic cable of a suspension bridge whose span is "L" and sag is "h." Find an equation for the cable.

b) The George Washington Bridge across the Hudson River in New York has a span of 3500 feet and a sag of 316 feet. Find an equation for the cable.

Thanks

2. Originally Posted by Rae
The shape of a flexible and inelastic cable supporting a load that is uniformly distributed horizontally, like the cables of a suspension bridge, is a parabola.

a) Place the origin of an xy-coordinate system at the lowest point of a parabolic cable of a suspension bridge whose span is "L" and sag is "h." Find an equation for the cable.

b) The George Washington Bridge across the Hudson River in New York has a span of 3500 feet and a sag of 316 feet. Find an equation for the cable.

Thanks
1. Draw a sketch.

2. The general equation of the parabola in question is:

$\displaystyle y = a\cdot x^2$

3. The point $\displaystyle P\left(\frac12 L\ ,\ h\right)$ belongs to the parabola.

4. Plug in the coordinates of P into the equation of the parabola and solve for a:

$\displaystyle h = a\cdot \left(\frac12 L\right)^2~\implies~a=\dfrac{4h}{L}$

5. Use these results to answer b).