Select ALL statements which are TRUE about the surface z x2

Select ALL statements which are TRUE about the surface z = x2 - y2. In the plane x = 0. its trace is the parabola z = -y2. In the plane y = 0, its trace is the parabola z - x2. In the plane z = 0, its trace is the pair of lines y = plusminus x. The surface is a hyperbolic paraboloid.

Solution

z = x^2-y^2 x=0 implies z = -y^2 y =0 implies z=x^2 z=0 implies x^2-y^2=0 so y=+x,y=-x in 3d its a hyperbolic parabollid so ALL OPTIONS ARE CORRECT