What Are the Hyperbolic Characteristics of the Quadratic Surface Z=x²-y²?

[nameVoid]

Z=x^2-y^2
The book is showing the trace for z=0 to be a hyperbola however I see y=x and y=-x

 

[tiny-tim]

hi nameVoid!

(try using the X² button just above the Reply box )

Z=x^2-y^2
The book is showing the trace for z=0 to be a hyperbola however I see y=x and y=-x

what book?

yes, Z = 0 is the crossed lines y = ±x

the curves for all other values of Z will be hyperbolas, fitting between y = ±x

 

[LCKurtz]

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.