The book is showing the trace for z=0 to be a hyperbola however I see y=x and y=-x
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yes, Z = 0 is the crossed lines y = ±x
the curves for all other values of Z will be hyperbolas, fitting between y = ±x
Also, since the lines ##y=\pm x## are the asymptotes for the family of level curves for that surface, they are sometimes considered to be degenerate hyperbolas.
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