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1、直线与椭圆的位置关系Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 学习目标： 1、熟练掌握椭圆的定义域几何性质，掌握直线与 椭圆的位置关系及弦长中点弦问题。 2、通过学习，培养学生逻辑
2、推理能力 3、通过学生互相交流学习，培养学生探索创新 、合作交流的学习精神。 重点难点：直线与椭圆的位置关系Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.
3、Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.问题问题2 2：怎么判断它们之间的位置关系？：怎么判断它们之间的位置关系？问题问题1 1：直线与圆的位置关系有哪几种？：直线与圆的位置关系有哪几种？drd00直线与椭圆相交
4、有两个公共点；(2)=0 直线与椭圆相切有且只有一个公共点；(3)0- (1)所以，方程（）有两个根，则原方程组有两组解 。题型一：直线与椭圆的位置关系Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pt
5、y Ltd.练习1.K为何值时,直线y=kx+2和曲线2x2+3y2=6有 两个公共点?有一个公共点?没有公共点?练习2.无论k为何值,直线y=kx+2和曲线交点情况满足( )A.没有公共点 B.一个公共点C.两个公共点 D.有公共点D题型一：直线与椭圆的位置关系Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyrigh
6、t 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.l mm题型一：直线与椭圆的位置关系Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspos
7、e Pty Ltd.oxy题型一：直线与椭圆的位置关系Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.oxy思考：最大的距离是多少？题型一：直线与椭圆的位置关系Evaluation onl
8、y.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.设直线与椭圆交于P1(x1,y1)，P2(x2,y2)两点，直线P1P2的斜率为k弦长公式：知识点2：弦长公式可推广到任意二次曲线Evaluation only.Eva
9、luation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例1：已知斜率为1的直线L过椭圆 的右焦点 ，交椭圆于A，B两点，求弦AB之长题型二：弦长公式Evaluation only.Evaluation only. Created w
10、ith Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.题型二：弦长公式Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created
11、with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004
12、-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例3 ：已知椭圆 过点P(2，1)引一弦，使弦在这点被平分，求此弦所在直线的方程. 解：韦达定理斜率韦达定理法：利用韦达定理及中点坐标公式来构造题型三：中点弦问题Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Cop
13、yright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例 3 已知椭圆 过点P(2，1)引一弦，使弦在这点被平分，求此弦所在直线的方程.点差法：利用端点在曲线上，坐标满足方程，作差构造出中点坐标和斜率点作差题型三：中点弦问题Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profi
14、le 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.知识点3：中点弦问题点差法：利用端点在曲线上，坐标满足方程，作 差构造出中点坐标和斜率Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-
15、2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.直线和椭圆相交有关弦的中点问题，常用设而不求的 思想方法 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 A
16、spose Pty Ltd.例3已知椭圆 过点P(2，1)引一弦，使弦在这点被平分，求此弦所在直线的方程.所以 x2+4y2=(4-x)2+4(2-y)2，整理得x+2y-4=0 从而A ,B在直线x+2y-4=0上 而过A,B两点的直线有且只有一条解后反思：中点弦问题求解关键在于充分利用“中点”这一 条件，灵活运用中点坐标公式及韦达定理，题型三：中点弦问题Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyr
