马鞍面有关的一道大学数学决赛题的解法研究

Study on Ways to Solve a Final College Mathematics Contest Problem concerning Sadlle Surfaces

第十届(2019年)全国大学数学竞赛数学专业组决赛第二题涉及求动直线的轨迹以及判断其轨迹的类型.针对该题提出多种解答思路,基于这些思路,又对该题的小问(I)与小问(II)分别给出4种解法,以期能在大学数学解析几何课程的教与学方面激起更多思考。

The second problem of the 10th(2019)China’s National College Mathematics Final Contest for Mathematics-majored students involves the trajectory of the varying straight line and the identification of the type of trajectory.A variety of idea are proposed to solve this question.Based on these ideas,four methods are provided to solve Question(I)and Question(II)of the concerned problem,with the desire to stimulate more thinking in the direction of teaching and learning analytic geometry in universities.