How do you solve this problem? The roof of a building is in the shape of the hyperbola y^2 -x^2 = 18, where x and y are in meters. Determine the distance, w, the outside walls are apart, if the height of each wall is 11 m.

                                      y^2-x^2 = 18
if you look at the graph of this hyperbola   
you just need to get the x coordinates where the line y= 11 ( hight )
is intersecting this hyperbolic curve.

To get the x coordinates put y = 11 in your equation
  121- x^2 = 18

  x^2 = 103

  x = +10.14  ,  -10.14   (approx)

clearly distance between walls is = 10.14 + 10.14 = 20.28 m   (approx)

Tell me what the answer is if you know ?