Then, by La Hire's Theorem, Q and R lie on the polar of P, so if P lies outside C , then the polar of P is the chord of contact QR . Suppose that C is a conic and that L is a line. Choose points A and B on L . Then, by La Hire's Theorem, A and B must lie on the polar of P, so the polar of P is the line L . Thus, every line is the polar of some point.
Definition Suppose that C is a conic, and that L is a line.
The pole of L with respect to C is the point with polar L . Duality with respect to a conic C . Suppose that C is a fixed conic. If X belongs to the set, then X' is the dual of X with respect to C . We say that a point and line are incident if the point lies on the line.