A problem asks me to do the following:
Find the equation of the surface generated by the normals to the surface $x + 2yz + xyz^2 = 0$ at all points on the Z axis.
I don't understand what this means! Sure, we can compute the normal to the given surface at any point (a line, no doubt) - but how do normals generate another surface, of which the question demands the equation? Please explain!