SOLUTION: A cable hangs in the form of a branch of a hyperbola between two poles that are 20 meters apart. The poles are 70 meters high and the cable has a sag of 2 meters midway between th

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A cable hangs in the form of a branch of a hyperbola between two poles that are 20 meters apart. The poles are 70 meters high and the cable has a sag of 2 meters midway between th      Log On


   

Question 1165039: A cable hangs in the form of a branch of a hyperbola between two poles that are 20 meters apart. The poles
are 70 meters high and the cable has a sag of 2 meters midway between the poles. Find the height of the cable
at a point 3 meters from one of the poles.
Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!


Draw a graph with the origin on the ground halfway between the two poles.

Then the vertex of one branch of the hyperbola is at (0,68), and one other point on that branch is (10,70). We are to find the point (7,y).

The equation of the hyperbola is

y%5E2%2Fa%5E2-x%5E2%2Fb%5E2+=+1

y%5E2%2F68%5E2-x%5E2%2Fb%5E2+=+1

The numbers in the problem are not "nice"; you will need a calculator to solve the problem.

You won't learn anything by having me do the calculations for you, so I leave that to you.

(1) Use the coordinates of the other point (10,70) in that equation to find b^2.

(2) Plug that value of b^2 in the equation, then solve for y when x=7.

Note: my answer, which is reasonable, is 68.987 to 3 decimal places