Pascal's hexagon

The six points are joined in the order A, B, C, D, E, F into a hexagon, and in that order the first side AB is opposite the fourth, DE, as BC is opposite EF and CD is opposite FA. Extended, the three pairs of opposite sides meet in the coral points X, Y and Z. Drag any of A to E and the ice-blue curve follows: it is the conic through those five points, since five points fix exactly one, and it can be an ellipse or be dragged into a hyperbola, with some points on one branch and the rest on the other. The ice-blue F can only travel along that curve. However you drag, X, Y and Z stay on the coral line, and “Crossings off one line” in the corner stays at 0.0000. Switch “Where F goes” to “Anywhere” and pull F a little off the curve: its distance from the curve is no longer 0, and the three crossings no longer lie on one line.