General expressions

Although the method is simple to describe, the algebra becomes messy when written in full generality. For example, suppose we use the second method, with three points \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\) none of which are at the origin. The three equations are \begin{gather} (Ax_1+By_1)^2+Cx_1+Dy_1=0\\ (Ax_2+By_2)^2+Cx_2+Dy_2=0\\ (Ax_3+By_3)^2+Cx_3+Dy_3=0 \end{gather} Solving the first two…