Conchoid of Dürer

Suppose two perpendicular lines are given, with intersection point O.

For concreteness we may assume that these are the coordinate axes and that O is the origin, that is (0, 0).

On the line QR, extended as necessary, mark points P and P' at a fixed distance a from Q.

Special cases include: The envelope of straight lines used in the construction form a parabola (as seen in Durer's original diagram above) and therefore the curve is a point-glissette formed by a line and one of its points sliding respectively against a parabola and one of its tangents.

[4] It was first described by the German painter and mathematician Albrecht Dürer (1471–1528) in his book Underweysung der Messung (Instruction in Measurement with Compass and Straightedge p. 38), calling it Ein muschellini (Conchoid or Shell).