About
In projective geometry, parallel lines meet at a point at infinity. A conic is any nondegenerate quadratic curve — all are projectively equivalent!
Pascal's Theorem: 6 points on a conic → 3 pairs of opposite sides meet on a line (the Pascal line)
Key Facts
Pascal (1640): For any hexagon inscribed in a conic, the 3 pairs of opposite sides are concurrent (meet in 3 collinear points).
Brianchon's dual: For any hexagon circumscribed about a conic, the 3 main diagonals meet at one point.
Conics: circle, ellipse, parabola, hyperbola — all sections of a cone, all projectively equivalent.
Drag the colored points to move them on the conic.