Ripple Simulation Orthogonal Conics Confocal ellipses and hyperbolas are mutually orthogonal. Two sets of parabolas sharing the same focus and axis but opposite in opening are mutually orthogonal too. Every theorem about lines has a dual about points, and vice versa. For Brianchon's theorem, start with six random tangents on a conic. Again label them in any order.
Consecutive tangents meet in a total of six points.
Connect the three pairs of opposite points, we'll have three lines, and they meet in a point. Both observations are correct, but in projective geometry parallel lines are said to meet at infinity. This convention reduces wordiness of theorems. From an advanced point of view, points and lines at infinity are parts of basic structure of projective geometry, they are no different than ordinary points or lines. A shortcut to prove Pascal's therorem is to first prove it for a circle then project the circle to a plane.