Plane Cubic Curves

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A plane cubic curve is a curve represented by an equation of the form

Ax3 + Bx2y + Cxy2 + Dy3 + Ex2 + Fxy + Gy2 + Hx + Iy + J = 0.

There are a total of 78 different species of plane cubic curves. The various species are distinguished by the shape of their branches and the positions of these branches relative to the asymptotes. These species have been grouped into 10 different genera. The animation above takes one through the 14 species having one diameter (monodiametral) belonging to the genus specified as "general redundant hyperbola" ( redundant hyperbola with three asymptotes containing a triangle). In the animation, the blue lines are the asymptotes and the green line is the diameter.

Animation created by

Dr. V N Krishnachandran

Vidya Academy of Science and Technology

Thrissur - 680 501, India.