Putnam 1949 A1

Answer either (i) or (ii):

(i) Let $a>0.$ Three straight lines pass through the three points $(0,-a,a), (a,0,-a)$ and $(-a,a,0),$ parallel to the $x-,y-$ and $z-$ axis, respectively. A variable straight line moves so that it has one point in common with each of the three given lines. Find the equation of the surface described by the variable line.

(II) Which planes cut the surface $xy+yz+xz=0$ in (1) circles, (2) parabolas?