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1、知识梳理与题型归类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.教学目标:1 了解圆锥曲线统一极坐标方程,明白方程中参数的 几何意义2 能根据圆锥曲线的基本量写出统一的极坐标方程, 能根
2、据统一极坐标方程判断圆锥曲线的类型并确定其 基本量.3 能利用圆锥曲线统一极坐标方程,计算圆锥曲线过 焦点的弦长 教学重点:方程中参数的认识与理解应用 教学难点:参数的灵活应用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 2004-20
3、11 Aspose Pty Ltd.圆锥曲线的统一极坐标方程为: 其中P为焦点到相应准线的距离, 称为焦参数.一、 取圆锥曲线的一个焦点为极点,极轴垂 直于相应的准线,但与其不相交,建立极坐标系B讨论构建知识阶段:圆锥曲线的极坐标方程的认识与理解P:抛物线标准方程中一次项系数一半,椭圆与双曲线中 焦点到相应准线的距离A 自学领悟知识阶段: 建立圆锥曲线的极坐标方程,并思考其中参数的意 义,坐标系建立的优越性.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.
4、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. Copy
5、right 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.三、如果极轴方向向右,表示椭圆时,极点是 它的左焦点,准线是它的左准线;表示双曲线时 ,极点是它的右焦点,准线是它的右准线.要注意圆锥曲线的统一极坐标方程在“格式”上的 “标准”要求，只有方程右边分母中的常数为1时COS 的系数绝对值才表示曲线的离心率，若该常数不是1， 要先化为1再判断，如：表示抛物线吗？不！椭圆。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Cl
6、ient 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.五、平面直角坐标系下，圆锥曲线方程中基 本量a,b,c,e与焦参数，e之间联系： e没改变，仍是离心率；即：椭圆和双曲线的统一极坐标方 程可以化为：这样,可以实现两类方程的互化,也为选择两类方程 解题,打开了通道.注意使用!P:抛物线标准方程中一次项系数一半, :抛物线, 椭圆与双曲线中焦
7、点到相应准线的距离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.O圆锥曲线的统一极坐标方程应用1基本量间的互求；圆锥曲线的判定，定量与 定位；实际应用。C应用知识阶段:Evaluatio
8、n 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
9、 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 Profil
10、e 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 Aspo
11、se 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.轨迹是椭圆,会回来的Evaluation only.Evaluation only. Created with Asp
12、ose.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.圆锥曲线的统一极坐标方程应用2求过焦点(极点)的弦长由于椭圆,抛物线的弦的两个端点极径均为正值, 所 以弦长都是 ;对于两个端点都在双曲线右支上 的弦,其端点极径均为正值, 所以弦长也是 ;对于 两个端点分别在双曲线左、右支上的弦,其端点
13、极径一 个为正值一个为负值, 所以弦长是 或 对于双曲线，为统一起见，一律用公式：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.ABO注意：叙述坐标系的建立时要合“要求”Evaluati
14、on 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.ABXOEvaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 C
15、lient 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.有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
16、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.直角坐标方程为:极坐标方程为:Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with As
