As usual we find the pedal curve of this curve with respect to the origin O, by drawing the normal from O to the tangent at each point of the tractrix locus. The locus of the normal-tangent intersections generates the pedal curve of the tractrix.


Click on the linked diagram at right, and then click on the ‘Animate’ button. The red driver point Q moves along the horizontal x-axis, and correspondingly, the points P trace out the tractrix. The points R trace out the pedal curve. Do you understand the construction? Do you recognize the pedal curve here?



The pedal curve resembles one side of a butterfly’s wings. It is not a curve we have seen before.