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CHASLES CUBIC

red: elliptic cubic with an oval
green: acnodal cubic blue: elliptic cubic with an infinite branch yellow: crunodal cubic magenta: cuspidal cubic 
Michel Chasles (1793, 1880): French mathematician. 
Cartesian equation:
, where a ¹ 0 (in other words, y
is a homogeneous polynomial of degree 3 in x and y).
Cubic. 
The homographic tranformation: reduces this Chasles cubic to the divergent parabola.
Like the divergent parabolas (as well as the cubic
hyperbolas), the Chasles cubics represent the perspectives of all cubics.
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© Robert FERRÉOL 2017