which are common tangents to both P = 0 and Q = 0 are tangent to C. So, by the AF+BG theorem, the tangential equation of C has the form HP + KQ = 0. Since C has class m, H must be a constant and K but have degree less than or equal to m−2. The case H = 0 can be eliminated as degenerate, so the tangential equation of C can be written as P + fQ = 0 where f is an arbitrary polynomial of degree m2. For example, let m = 2, P1 = (1,0), and P2 = (−1,0). The tangential equations are X + 1 = 0 and X − 1 = 0 so P = X2 − 1 = 0. The tangential equations for the circular points at infinity are X + iY = 0 and X − iY = 0 so Q = X2 +Y2. Therefore, the tangential equation for a conic with the given foci is X2 − 1 + c(X2 +Y2) = 0, or (1+ c)X2 + cY2 = 1 where c is an arbitrary constant. In point coordinates this becomes References Conic sections Geometric centers