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
x2 = 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: x2 = 100y.
