Try to knock out possibilities. At x=0, you are in the yz-plane, and you know that in the plane, you will have z=f(y) and z=-f(y). Plugging in x=0 to B gives z^2=f(y), which must be wrong. C gives z^2=|f(y)|, which is wrong. D is a formula that lies entirely in the yz-plane (so is not a surface of revolution). E rotated the original equation to either to xy- or xz- plane. Hence, A is the only remaining answer.