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众所周知,求圆锥曲线标准方程的常规方法是:首先确定标准方程的类型,并将其用有关参数表示出来(设方程),然后再结合问题的条件建立含参数的等式,求得参数的值代入所设方程,即:一定性,二定量。如果题目中缺少定性条件,则要根据其所有可能,进行分类讨论,运算量大,较为繁琐。这时,若能抓住问题的具体特征,整体思考,巧设方程,常常可以简化讨论,减少运算量,使我们收到事半功倍的效果。
As is known to all, the conventional method for finding the standard equation of a conic section is to first determine the type of the standard equation and express it with the relevant parameters (set equations). Then combine the conditions of the problem to establish equations with parameters to obtain the values of the parameters. Substitute into the equation set, that is: certain, two quantitative. If there is a lack of qualitative conditions in the topic, it is necessary to discuss the classification based on all its possibilities. The calculation is large and cumbersome. At this time, if we can grasp the specific characteristics of the problem, think about it wholeheartedly, and formulate equations, we can often simplify the discussion and reduce the amount of computation, so that we can get a multiplier effect.