Guadou principle is the principle of friendship. If the distance ratio between two moving points and a fixed point is a fixed value and the included angle is a fixed angle, the trajectories of the two moving points are the same. Guadou principle is a master-slave linkage trajectory problem.

The driving point is called melon and the driven point is called bean. Melons move in a straight line, and so do beans. The movement of the melon is round, so is the trajectory of the bean. The key is to make the trajectory of the driven point, and make the special point of the driven point according to the special position of the driving point, so as to connect the trajectories.

Name source

As you sow, you reap, and the relationship between driving point and driven point is vividly described. It is easy to find that the movement of point A leads to the movement of point C.

And if we look at the problem from another angle, we will find that every point C has a corresponding point A, and point C can be regarded as a point A rotated 90 counterclockwise. In other words, the trajectory of A is a hyperbola, so the trajectory of C must also be a hyperbola, which is obtained by rotating the trajectory of A 90 counterclockwise.

By extension, as long as it is the three major transformations of the image, if the trajectory of the active point is a straight line, can it be concluded that the trajectory of the driving point is also a straight line? If the trajectory of the driving point is a circle, then the trajectory of the driven point should also be a circle. This is the so-called vivid name, as you sow, so you reap.