Joachimsthal's Equation

Using Clebsch-Aronhold Notation,

$$\xi_1^n a_y^n+\xi_1^{n-1}\xi_2a_y^{n-1}a_x+{\textstyle{1\ove... ...n-2}a_x^2+\ldots+n\xi_1\xi_2^{n-1}a_ya_x^{n-1}+\xi_2^na_x^n=0.$$

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 89, 1959.