Hyperboloidic volcano

Algebra Level pending

The surface of a volcano can be described by the lower sheet of a hyperboloid of two sheets with the equation x 2 + y 2 ( z 4 ) 2 = 1 x^{2}+y^{2}-(z-4)^{2} = -1
Calculate the height of the volcano.

Clarification: The height of the volcano is described by the maximum z z - value of the equation.

3 4 5 2

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