Question

is x^2+y^2-z^2=1 an ellipse or hyperbola?

Answer 1

\[x ^{2}+y ^{2}-z ^{2}=1\] You sure this is what you mean? It's neither. It's a geometrical figure called a "one-sheeted hyperboloid"

Answer 2

It looks like this

Answer 3

well when I find traces I have to find what each plane make so either an ellipse or hyperbola, which confuses me because that shape is neither :/

Answer 4

If you cut the shape horizontally at any point it will look like an ellipse. If you cut it vertically at any point it will look like a hyperbola.