On some loci of lines in plane kinematics

In recent years generalizations of the Ball and Burmester problems of the following type have been considered: if a plane q moves in a prescribed manner with respect to a fixed plane Q, what is the locus of a point in q such that up to seven positions lie on a conic in Q. In this paper we derive the locus of a line in q such that either its five positions in Q are tangent to a parabola, or that its six positions are tangent to a conic. The loci are respectively of the second and the fourth class.