Focus chord and conic curves (ellipse, hyperbola and parabola) of 1 have the shortest paths.
2. The relationship between the circle with focus chord diameter and the corresponding directrix: ellipse separation; Hyperbola-intersection point; Parabolic tangency.
3. The half path (half of the path) is the harmonic median, in which the focus chord is divided into two focal radii by the focal point.
4. The product of the two focal radii that make up the focus chord is directly proportional to the chord length of the focal points.
Extended data:
The two tangents at the two ends of the focus chord intersect the directrix, and the line connecting the intersection and the focus is perpendicular to the focus chord. On the other hand, any point on the collimation line is two tangents of the conic, and the straight line connecting the two tangents will pass through the focus.
One end passing through focus chord serves as the perpendicular of the directrix, and the vertical foot is connected with the other end of focus chord, so the connecting line bisects the line segment between the focal point and the intersection of the directrix and the axis.
Let focus chord AB (hyperbola is the same branch) be non-parallel to the axis, where the vertical line intersects the X axis at G and F is the corresponding focus, then AB:FG is a fixed value of 2/E.