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Conics

  • Definition: Ellipses, hyperbolas, and parabolas are called conics. They are loci in R^2 defined by quadratic equations f=0 where f(x_1,x_2)=(a_11)(x_1)^2 + 2(a_12)(x_1)(x_2) + (a_22)(x_2)^2 + (b_1)(x_1) + (b_2)(x_2) + c, and the coefficients a_ij, b_i, and c are real numbers.

    Source: Algebra, second edition by Michael Artin

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