The Conical Pole P of a line L wrt some conic CO is the intersection point of the tangents to CO at the intersection points of CO with L. In this construction P is called the pole and L is called the polar.

This construction is very intuitive. However there is a flaw in the definition because the pole cannot be constructed under all circumstances. For example when CO is some ellipse and L is not intersecting the ellipse, then the construction fails.

Therefore another construction is made that includes the result of the first construction:

The pole of some line L wrt some conic (see CO-Tf1) is the intersection point of the polars of two random points from line L.

This construction is very intuitive. However there is a flaw in the definition because the pole cannot be constructed under all circumstances. For example when CO is some ellipse and L is not intersecting the ellipse, then the construction fails.

Therefore another construction is made that includes the result of the first construction:

The pole of some line L wrt some conic (see CO-Tf1) is the intersection point of the polars of two random points from line L.