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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.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 Pty 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. Copyright 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 Aspose 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 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.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.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.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 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.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 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 2004-2011 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. Copyright 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 Profile 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 2004-2011 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 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.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
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