The set of ideal points is the ideal line or line at infinity . A detailed description is given on the ideal points page. This allows us to unify classical theorems. If the chord AB of C passes through O, then the tangents at A and B are parallel. Provided we allow ideal points and lines, every point has a line associated with it by the Key Theorem.
Definition Suppose that C is a conic, and that P is any point.
The polar of P with respect to C is the line specified in the Key Theorem. Suppose that C is a conic, and that P and Q are points. Since the polars at Q and R are the tangents at these points, P lies on both polars. 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.