Problem Solving

6. Under certain condition, a cable which hangs between two supports can be closely approximated as being parabolic. Assuming that this cable hangs in the shape of a parabola, find its equation if a point 10ft horizontally from its lowest point is 1.0ft above its lowest point. Choose the lowest point as the origin of the coordinate system.

Solution:

First draw x and y axes and the parabola. The general equation for a parabola is

x^{2} = 4py

We need to determine p. All we need for this is one data point.

Use (10, 1).

(10)^{2} = 4p(1) So p = 25.

Then: x^{2} = 100y.