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Ever wondered what does it mean that a parabola is tangent to the line of infinity, or that a hyperbola cuts it twice?



# Parabola - tangent to the line of infinity
p = x^2-y

# Hyperbola - cuts twice the line of infinity
p = x^2-y^2+16

# Singular Cubic - has a point of inflection tangent to the line of infinity
p = x^2+x^3/2-y^2