课本例题是重要的教学资源,充分利用这一资源,对减轻学生负担、培养学生提出问题与解决问题的能力,是一条有效的途径.人教版A版选修4—4《坐标系与参数方程》第37页例2就是这样一道好题,笔者力寻其简解的依据,并把问题在知识的最近发展区内作进一步的推广,解决了与原问题相关的一类新问题,使例题效益达到最大化.题目经过点M(2,1)作直线l,交椭圆x216+y24=1于A,B两点.如果点M恰好为线段AB的 Textbook example is an important teaching resources, make full use of this resource, to reduce the burden on students, to develop students’ ability to ask questions and solve problems is an effective way. PEP P version elective 4-4 "coordinate system and parametric equation Example 2 on page 37 is such a good topic, the author is trying to find out the basis for its briefing, and the problem in the knowledge of the nearest development zone for further promotion, to solve a problem with a new class of problems related to the original problem The maximization of efficiency.The subject goes through the point M (2,1) as a straight line l, intersecting the ellipse x216 + y24 = 1 at A and B. If the point M is exactly AB