SOLUTION: A cable suspended between two posts that are the same height and 10 meters apart has a sag of 1 meter. If the cable hangs in the form of a parabola, find its equation, taking the l

Question 995545: A cable suspended between two posts that are the same height and 10 meters apart has a sag of 1 meter. If the cable hangs in the form of a parabola, find its equation, taking the lowest point as the origin.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A cable suspended between two posts that are the same height and 10 meters apart has a sag of 1 meter. If the cable hangs in the form of a parabola, find its equation, taking the lowest point as the origin.
---------
Sketch the figure on an x/y coordinate system.
---------
Place the lowest point at (0,0)
The top of the posts will be at (-5,10) and (5,10)
-----
Procedure::
Form:: ax^2 + bx + c = y
Using (-5,10) you get: 25a - 5b = 10
Using (5,10) you get: 25a + 5b = 10
-------
50a = 20
a = 2/5
-----
Solve for "b"::
25a + 5b = 10
25a + 2 = 10
25a = 8
a = 8/25
-----
Equation:
y = (8/25)x^2 + (2/5)x
-----------
Cheers,
Stan H.
----------

RELATED QUESTIONS
A cable suspended between two posts that are the same height and 20 meters apart has a... (answered by Alan3354)

A cable suspended form supports that are the same height and 600ft apart has a sag of... (answered by ankor@dixie-net.com)

A cable hangs in the form of a branch of a hyperbola between two poles that are 20 meters (answered by greenestamps)

A cable hangs in the form of a branch of a hyperbola between two poles that are 20 meters (answered by ikleyn)

a cable of a suspension bridge is suspended between two towers that are 1500 m apart and... (answered by ikleyn)

Bridge design: A cable of a suspension bridge is suspended (in the shape of parabola)... (answered by Alan3354)

A cable of a suspension bridge is suspended (in the shape of the parabola) between the... (answered by Alan3354)