As usual we find the caustic curve of the tractrix with respect to the origin O, by drawing the normal at each point P of the tractrix locus, and reflecting line OP in this normal. The envelope of the reflected lines forms the caustic curve.


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 maroon lines generate the caustic curve as an envelope. Do you understand the construction? Dsecribe the caustic curve here.


The caustic curve is a pleasant three-cusp curve, symmetric about the x-axis. It is not a curve we have seen before.