Second order curve/Definition

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Second order curve [r]:

A planar curve defined by a quadratic equation: $ax^{2}+bxy+cy^{2}+dx+ey+f=0$  in the affine plane, or $\sum _{i,j=0}^{2}a_{ij}x_{i}x_{j}=0$  in the projective plane; also called a conic because of its geometrical generation.