Given a reference triangle Δ A B C and a point P, the triple (x, y, z), with x = P A, y = P B and z = P C representing the distances from P to the vertices of the reference triangle, is the tripolar coordinates of P. The tripolar coordinates satisfy (a^2 + b^2 - c^2)(x^2 y^2 + c^2 z^2) + (a^2 - b^2 + c^2)(b^2 y^2 + x^2 z^2) + (-a^2 + b^2 + c^2)(a^2 x^2 + y^2 z^2) - (a^2 x^4 + b^2 y^4 + c^2 z^4) - a^2 b^2 c^2 = 0 (y^2 + z^2 - a^2)^2 x^2 + (x^2 + z^2 - b^2)^2 y^2 + (x^2 + y^2 - c^2)^2 z^2 - (y^2 + z^2 - a^2)(x^2 + z^2 - b^2)(x^2 + y^2 - c^2) - 4x^2 y^2 z^2 = 0 (Euler 1786).