over the towers of a bridge a cable is hung in the form of a parabola, have their tops 30 meters above the road way are 200 meters apart. If the cable is 5 meters above the road way at the centre of the bridge, then the length of the vertical supporting cable 30 meters from the centre is

Explanation

Let us assume that lowest point of cable as origin and equation of parabola will be `x^2
=4ay`

Given, tower of bridge is `30` meters above the road-way and lowest point is 5 meters above the road.

Then in equation y-coordinate of top of tower is 25 meters and x-coordinate is 100 meters,

from equation we get `100^2=4a(25)`

`implies a=100`

Now,length of the vertical supporting cable 30 metres from the centre is given by `y+5` where y is given by `30^2=4(100)(y)`

`implies y= 9/4`

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