Q. 13

The towers of bridge, hung in the form of a parabola, have their tops 30 m above the roadway, and are 200 m apart. If the cable is 5 m above the roadway at the center of the bridge, find the length of the vertical supporting cable, 30 m from the center.

Answer :

Given: Top of the towers are 30 m above the roadway and are 200 m apart. Cable is 5 m above the roadway at center.


Need to find: Length of the vertical supporting cable, 30 m from the center.



A and B are the top of the towers. AE and BF are the height of the towers. H is the center of the bridge. HI is the 5 m above from the roadway.


Let, the equation of the parabola be: x2 = 4a(y – b)


Here b = 5. So, x2 = 4a(y – 5)


Here, AB = 200 m and BF = 30 m.


So, the coordinate of the point B is (100, 30)


The point is on the parabola.


Hence, x2 = 4a(y – 5)


10000 = 4a (30 – 5)


10000 = 4a x 25


a = 100


Now we need to find, the length of the vertical supporting cable, 30 m from the center.


The x-coordinate of the point, 30 m from the center, is 30.


So, 30 x 30 = 4a (y – 5)


900 = 400 (y – 5)


y – 5 =


y =


So, the length of the vertical supporting cable is m = 7.25 m


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