Question

A cable of a suspension bridge isin the form of a parabola whose span is $40mts.$ The road way is 5 mts below the lowest point of the cable. An extra support is provided across the cable 30 mts above the fround level. Find the length of the support if the height of the pillars are 55 mts.

Answer 1

To write, $x^2=4ay$
Since, the span of the parabola is $40mt.$
So, $x-co-ordinate$ of $A=20$
The height of the pillars are $55$ meters$=AB$

So the co-ordinates of point $A=(20,50)$
Let the support be $PQ$
So, equation of the parabola gets reduced to

$x^2=8y$

Identifying the point $Q(x_1,25)$

$x_1=10\sqrt{2}$

$PQ=2x_1=20\sqrt{2}mts$