Answer:
Hyperbola
Step-by-step explanation:
Consider [tex]x=k.[/tex]
Substitute [tex]x=k[/tex] in given equation [tex]x^2+y^2-z^2=81[/tex]
[tex]k^2+y^2-z^2=81[/tex]
[tex]\Rightarrow y^2-z^2=9^2-k^2[/tex]
[tex]\Rightarrow y^2-z^2=(9-k)(9+k)[/tex]
Here, different orientation for [tex]-9<k<9[/tex] then [tex]-9<k[/tex] or [tex]k<9.[/tex]
Hence, the surface equation represents a trace of the hyperbola.
