A cable suspended between two posts that are the same height and 10 meters apart has a sag of 1 meter. If the cable hangs in the form of a parabola, find its eq

Question

A cable suspended between two posts that are the same height and 10 meters apart has a sag of 1 meter. If the cable hangs in the form of a parabola, find its equation

Answer 1

There is no unique answer, however, the easiest answer assumes that the parabola passes through three points:

( 0 , 0)

(-5, 10)

(+5, 10)

To pass through the origin (0,0), the equation must be of the form y = kx²

To pass through the point (5,10), k must be such that

10 = k(5²)

or

k = 10 / 25 = 2 / 5

Thus we have the simplest solution:

y = (2/5) x²

We can place the vertex anywhere, such as at (a,b). In that case, our answer would be

y - b = (2/5)(x - b)²