Droussent cubic K(008)
Here we have triangle and Droussent cubic the black one on the figure and we take point on it. After that we cojugate this point isogonal and we get point . By using GeoGebra we get another cubic the blue one on the figure which is isogonal transform of Droussent cubic.
Barycentric equation
Proof
We again substitude , and with , and .
And this is the equation of the K108 cubic which means that Droussent cubic is isogonal transform of K108.