The class of curve known as Dürer's conchoid appears in Dürer's work *Instruction in Measurement with Compasses and Straight Edge* (1525) and arose in investigations
of perspective. Dürer constructed the curve by drawing lines and of length 16 units through and , where . The locus of and is the curve, although Dürer found only one of the
two branches of the curve.

The envelope of the lines and is a parabola, and the curve is therefore a glissette of a point on a line segment sliding between a parabola and one of its tangents.

Dürer called the curve "muschellini," which means conchoid. However, it is not a true conchoid and so is sometimes called Dürer's shell curve. The Cartesian equation is

There are a number of interesting special cases. For , the curve becomes the line pair together with the circle . If , the curve becomes two coincident straight lines . If , the curve has a cusp at .