Let [i]S[/i] be any curve and let [i]A[/i] be a fixed point. If a straight line is drawn through [i]A[/i] to meet [i]S[/i] at [i]Q[/i], and if [i]P[/i] and [i]P[/i]' are points on this line such that [br][br][center][i]P'Q[/i] = [i]QP[/i] = [i]k[/i]      (a constant)[/center]the locus of [i]P[/i] and [i]P'[/i] is called a [i][b]conchoid[/b][/i][b][i] of S with respect to A[/i][/b].

The conchoid of a circle of radius [i]r[/i] with respect to a point within it.

A conchoid of a parabola with respect to the focus

A conchoid of an ellipse or hyperbola with respect to a focus.