A NOTE ON THE THIRD FOCUS OF THE CARTESIAN OVAL

The subject of this paper is the determination of the coordinate of the third focus of the Cartesian oval. For this purpose, the Computer Algebra System Maple was used with the use of the pseudo-resultant technique and Groebner bases. The third focus formula and consistency conditions for determining the third focus were obtained. The algebraic formula for the coordinate of the third focus when the focal points with general coordinates p, q, r were obtained and the consistency conditions for defining the Cartesian oval through the third focus were also presented.