Notes: Coefficients A, B, C are unaffected by translation. If the starting coefficients are <A, B, C, D', E', F'>, and the conic is in the standard form [math] (1a) \;\;\;\;\; f(x,y) = A x^2 + Bxy + Cy^2 + D'x + E'y + F' = 0 [/math] The transformation vector is [b]u[/b] = (Δx, Δy), And if the transformed coefficients are <A, B,C,D, E, F>, then the curve 1a can be written [math] (1b) \;\;\;\;\; f(\bar x,\ bar y) = A \bar x^2 + B\bar x \bary + C \bar y^2 + D \bar x + E \bar y + F = 0, [/math], [math] \;\;\;\;\;\;\; {\small \bar x = x\!- Δx, \;\;\bar y = y - Δy}[/math] The same procedure can be used to translate the curve. Leaving the coordinates in (x, y) --(local origin (0,0)) --, [math] (2) \;\;\;\;\; g(x, y) = A x^2 + Bx y + C y^2 + D x + E y + F = 0, [/math] translates the curve by -[b]u[/b].