This topic mainly examines the definition, geometric properties, cosine theorem, mathematical thought of transformation of hyperbola, as well as the comprehensive application ability and calculation ability of candidates. If you blindly want to do it with vectors, you will fall into the trap carefully arranged by the questioner and fall into endless calculation.

First of all, in the process of using vectors, it is very difficult to transform known conditions into solutions, such as the length of real axis, the definition of hyperbola and so on.

Secondly, the application of vector solution in this problem seems simple (because all the necessary conditions seem to be met), and as long as (x,) is set, you will exclaim "Wow ~ what a simple algebraic operation ~ ~", but in fact, you will find that not only the vector operation but also the transformation between XY should be considered in the operation process, and then the first term of x and y will appear, so …

This question takes vector as the most means to examine the examinee's understanding and flexible application of hyperbola concept. In high school mathematics, vectors must be tools, especially in the number of articles. Be sure to consider everything when you do the problem. Using vectors as a bridge, we must finally return to geometric properties. Remember! !