In fact, the study of Arrhenius circle mainly starts from the hidden circle and the maximum value. Related to the maximum value, similar to the advanced version of "Hu Bugui Problem". Therefore, it also determines its handling method, which will be more thoughtful and thoughtful. The problem of hidden circle mainly examines students' understanding and memory of the conditional characteristics of circle. And this is destined to be faced by high school students. Because of the comprehensive questions, a high school student's adaptability and comprehensive ability can be better examined.
Model building:
If two points A and B on the plane are known, then all points P that conform to PA/Pb = k (k > 0, k≠ 1) will form a circle. This conclusion was first discovered by the ancient Greek mathematician apollonius, and it is called a circle.
Circle profile:
It is the abbreviation of apollonius Circle. If two points A and B on the plane are known, then the trajectories of all points P that satisfy PA/PB=k and are not equal to 1 are all circles, and their diameter is the fixed ratio m: n of the connecting line between the two points of the line segment AB. This trajectory was first discovered by the ancient Greek mathematician apollonius, so it is called a circle.
Model background:
The maximum value of 1 and "PA+K Pb" is a hot and difficult issue in the senior high school entrance examination in recent years. When the value of k is 1, it can be transformed into the shortest sum problem of "PA+PB", which can be dealt with by our common "horse drinking problem" model, that is, it can be transformed into an axisymmetric problem. However, when k is an arbitrary positive number other than 1, the problem will not be solved by the conventional axisymmetric thought.
Therefore, we must change our thinking. The processing of this kind of problem is usually classified according to the different images where the moving point is located, and it is generally divided into two types of research. That is, point р moves in a straight line and point P moves in a circle. Among them, the type of point р moving along a straight line is called "Hu Bugui" problem; The motion type of point р on the circumference is called Archimedes circle problem.