Let H be the surface with equation x^{2}+y^{2}z^{2} = 1. Since x^{2}+y^{2}= z^{2}1, the points on H have z^{2} ≥ 1, i.e. z ≥ 1 or z ≤ 1. Thus, the surface H consists of two disjoint parts  the sheets of H. If k > 1, H meets the plane z = k in the circle x^{2}+y^{2} = k^{2}1, z = k. Also from this rearrangement, H has radial symmetry about the zaxis. Now, H meets the xzplane (y=0) in the curve x^{2}z^{2} = 1. If we write this in the form z^{2}x^{2} = 1, we see that the curve of intersection is a hyperbola. With the radial symmetry, we observe that H is obtained by rotating this hyperbola about the zaxis. The sheets of H derive from the branches of the hyperbola. Also, the asymptotes x±z =0, y=0 of the hyperbola generate the cone C : x^{2}+y^{2}z^{2} = 0. 
