Normals to Parabola across external point, Barton's
normals across external point
Barton's method uses the equations to find the center of a circle that passes across vertex and normals. See https://archive.org/details/jstor-2971798/page/n1/mode/2up
To build the center constructively, we bisect to get points C and D, and also E. The coordinate along the axis is the length of F'E translated to the vertex.