The Kobe Port Tower is a hyperbolic telecommunications tower in Kobe, Japan. It has a cross section that is a hyperbola. The height of the tower is 108 meters and the narrowest point is 65.5 meters above the ground. At that narrowest point the tower is only 8.2 meters wide. The diameter of the base of the tower is 25 meters. Use this information to place a hyperbola in a coordinate system and reason out its equation. Show all work on this page.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.