# NCERT Class 11 Mathematics Solutions: Chapter 11 –Conic Sections Miscellaneous Exercise 11 Part 2

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1. The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and long is supported by vertical wires attached to the cable, the longest wire being and the shortest being . Find the length of a supporting wire attached to the roadway from the middle.

Answer:

The vertex is at the lowest point of the cable.

The origin of the coordinate plane is taken as the vertex of the parabola, while its vertical axis is taken along the positive y-axis.

This can be diagrammatically represented as

are the longest and the shortest wires, respectively, attached to the cable.

is the supporting wire attached to the roadway, from the middle.

Here, , and

The equation of the parabola is of the form (as it is opening upwards).

The coordinates of point are .

Since is a point on the parabola,

Equation of parabola

The x-coordinate of point is .

So, at

So, the length of the supporting wire attached to the roadway from the middle is approximately .