For planar polynomial homogeneous real vector field X = (P,Q) with deg(P) = deg(Q) = n some algebraic equations of degree n 1 with GL(2,R)-invariant coefficients are constructed. A recurrent method for the construction of these coeffi- cients is given. In the generic case each real or imaginary solution si (i = 1, 2, . . . , n 1) of the main equation is a value of the derivative of the slope function, calculated for the corresponding invariant line. Other constructed equations have, respectively, the solutions 1/si, 1 − si, si/(si − 1), (si − 1)/si, 1/(1 − si). The equation with the solu- tions (n 1)si −1 is called residual equation. If X has real invariant lines, the values and signs of solutions of constructed equations determine the behavior of the orbits in a neighbourhood at infinity. If X has not real invariant lines, it is shown that the necessary and sufficient conditions for the center existence can be expressed through the coefficients of residual equation.