Analysis of the offset to a parabola Original Research Article

Wei Lü has recently constructed a proper rational parameterization for the two-sided offset to a parabola—indicating that this locus, an irreducible curve of degree n = 6, is of genus 0. The theory of algebraic curves then requires that the parabola offset have 12(n−1)(n−2) = 10 double points. One affine node and six affine cusps are readily identified by geometric arguments; we show that the remaining three double points are accounted for by a non-ordinary double point at infinity, having double points in its first and second neighborhoods.