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如图,△AOB的∠AOB=π/3,AB在直线:x=3上移动。求△AOB的外心的轨迹方程,并说明轨迹是什么图形。这是湖南省1986年高考预选题中的一道题。这道题既有对基础知识的要求,又有对思维能力的考查,有一定的综合性与灵活性,对解题教学是很有启发的。下面结合学生解这道题中的一些情况,谈一些认识与体会。解法一:设△AOB的外心为P(x,y),因A,B在直线x=3上移动,可设A、B的坐标分别为(3,t_1),(3,t_2)。易知,OA、AB的垂直平分线方程分别为
As shown in the figure, △AOB ∠AOB=π/3, AB moves on the straight line: x=3. Find the trajectory equation of the outside of AOB, and explain what the trace is. This is a question in the 1986 college entrance examination pre-selected questions. This question has both the requirements for basic knowledge and the examination of thinking ability. It has a certain degree of comprehensiveness and flexibility, and it is instructive for solving problem teaching. The following will combine students to solve some of the problems in this question and discuss some understandings and experiences. Solution one: Let ΔAOB be the outer center of P(x,y). Since A and B move on the straight line x=3, the coordinates of A and B can be set to (3, t_1) and (3, t_2) respectively. It is easy to know that the vertical bisector equations for OA and AB are