This curve was investigated by Tschirnhaus, de L'Hôpital and Catalan. As well as Tschirnhaus' cubic it is sometimes called de L'Hôpital's cubic or the trisectrix of Catalan.

The name Tschirnhaus's cubic is given in R C Archibald's paper written in 1900 where he attempted to classify curves.

Tschirnhaus's cubic is the negative pedal of a parabola with respect to the focus of the parabola.

The caustic of Tschirnhaus's cubic where the

radiant point is the pole is

Neile's semi-cubic parabola.

Cartesian equation:

3a y^{2} = x(x-a)^{2}

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