(Solved): An hyperboloid is a 3 D shape whose cross sections are hyperbolas. A nuclear cooling tower is in th ...

An hyperboloid is a 3 D shape whose cross sections are hyperbolas. A nuclear cooling tower is in the shape of a portion of a hyperboloid. A cross section of the cooling tower can be modeled by the hyperbola shown below, centered at the origin and opening left/right. If the smallest diameter of the cooling tower is $180\mathrm{m}$ and the diameter is $195\mathrm{m}$ at its highest point, $80\mathrm{m}$ above, write the equation of the hyperbola. (Diagram is not to scale.)