[size=85]Here we have triangle [math]ABC[/math][/size] [size=85]and Droussent cubic the black one on the figure and we take point [math]M[/math] on it. After that we cojugate this point isogonal and we get point [math]N[/math]. By using GeoGebra we get another cubic the blue one on the figure which is isogonal transform of Droussent cubic. [/size]

[math]\sum_{cyclic}\left(b^4+c^4-a^4-b^2c^2\right)x\left(y^2-z^2\right)=0[/math]

We again substitude [math]x[/math], [math]y[/math] and [math]z[/math] with [math]a^2zy[/math], [math]b^2xz[/math] and [math]z^2xy[/math].[br][math]\sum_{cyclic}\left(b^4+c^4-a^4-b^2c^2\right)x\left(y^2-z^2\right)=0[/math][br][math]\sum_{cyclic}\left(b^4+c^4-a^4-b^2c^2\right)a^2yz\left(b^4x^2z^2-c^4x^2y^2\right)=0[/math][br][math]\sum_{cyclic}\left(b^4+c^4-a^4-b^2c^2\right)a^2x^2yz\left[-\left(b^4z^2-c^4y^2\right)\right]=0[/math][br][math]-xyz\sum_{cyclic}\left(b^4+c^4-a^4-b^2c^2\right)x\left(b^4z^2-c^4y^2\right)=0[/math] [size=85]And this is the equation of the K108 cubic which means that Droussent cubic is isogonal transform of K108.[br][/size][br][br]