Hello, sureshrju!

The description is not clear,

but I can guess the design of the bridge.

The Lion's Gate bridge in Vancouver, BC, is a suspension bridge that spans 1516m.

Large cables are attached to the tops of the towers, 50 m above the road.

The road is suspended from the large cables with small vertical cables, the smallest one being 2m.

Find a quadratic equation to model the large cable shape.

Place the bridge on coordinates axes with the center of the bridge at the Origin.

Code:

:
* : *(758,50)
| : |
|* : *|
| * : * |
| * : * |
| * |
| (0,2) |
| : |
| : |
- - * - - - + - - - * - -
-758 0 758
:

The general form of this parabola is: .$\displaystyle f(x) \:=\:ax^2 + c$

We have two point on the parabola: .$\displaystyle (0,2),\;(758,50)$

$\displaystyle f(0) = 2:\;\;0^2a + c \:=\:2 \quad\Rightarrow\quad c \;=\;2$

$\displaystyle f(758,50):\;\;758^2a + 2 \:=\:50 \quad\Rightarrow\quad a \:=\:\frac{12}{143,\!641}$

Therefore, the equation is: .$\displaystyle f(x) \;=\;\frac{12}{143,\!641}\,x^2 + 2$