This is my own try at making this work with the substitution method. It’s manageable if you know the equation well, but the steps get really tedious with a complex quadratic equation.
L = m x + n y;
ellipseOriginal = (x + x0)^2/a^2 + (y + y0)^2/b^2 == 1;
ellipseHomogenized1 =
ellipseOriginal /. {x0 -> x0*L, y0 -> y0*L, 1 -> L^2}
How to use code to automatically generate such a homogeneous quadratic equation by combining the linear equation and the quadratic curve?
