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1、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.理解双曲线的定义；2.能根据定义推导出双曲线的标准方 程；3.掌握焦点在x轴和焦点在y轴两种情 形下双曲线的标准方程；4.掌握a
2、、b、c三者之间的关系，并能 够在解题中熟练应用。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 2004-2011 Aspose Pty Ltd.1. 回顾 椭圆的定义和 等于常数2a ( 2a|F1F2|)的点的轨迹.平面内与两定点F
3、1、F2的距离的2. 引入问题：差等于常数 的点的轨迹是什么呢？平面内与两定点F1、F2的距离的动 画我们一起看一下课本116页8-11的演示实验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 L
4、td.P= M |MF1 | - | MF2| = 2a P= M |MF1 | - | MF2| =2a P= M |MF1 | - | MF2| |=2a 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
5、e Pty Ltd. 两个定点F1、F2双曲线的焦点; |F1F2|=2c 焦距.平面内与两个定点F1，F2的距离的差等于常数 的点的轨迹叫做双曲线.（小于F1F2）定义:oF2F1MEvaluation 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 200
6、4-2011 Aspose Pty Ltd.|MF1|MF2|=|F1F2|时，M点一定在上图中的射线F1P ，F2Q 上，此时点的轨迹为两条射线F1P、F2Q。 常数大于|F1F2 |时常数等于|F1F2|时|MF1|MF2| |F1F2|F2F1P MQ M是不可能的，因为三角 形两边之差小于第三边。此时无轨迹。此时点的轨迹是线段F1F2的垂直平 分线。则|MF1|=|MF2|F1F2M常数等于0时 若常数2a= |MF1|MF2| =0动 画说明：Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.
7、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.总结： （F1、F2是两定点, |F1F2| =2c (0c，动点M的轨迹 .Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Create
8、d 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.1. 建系设点.F2F1MxOy2. 写出适合条件的点M的集合；3. 用坐标表示条件，列出方程；4. 化简.求曲线方程的步骤：如何求双曲线的标准方程？Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.C
9、reated 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.xyo设M（x , y）,双曲线的焦距为2c（c0）,F1(-c,0),F2(c,0)常数=2aF1F2M即 (x+c)2 + y2 - (x-c)2 + y2 = + 2a_以F1,F2所在的直线为X轴，线 段F1F2的中点为原点建立直角坐标系1. 建系.2.设点3.列式|MF1| - |MF2|= 2a如何求这条曲线的方程？4.
10、化简.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.oF2FMyx 1Evaluation only.Evaluation only. Created with Aspose.Slide
11、s 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.F2F1MxOyOMF2F1xy双曲线的标准方程想一想：焦点在y轴上的双曲线的标准方程是什么？Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client P
12、rofile 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：如何判断双曲线的焦点在哪个轴上？问题：如何判断双曲线的焦点在哪个轴上？练习：写出以下双曲线的焦点坐标练习：写出以下双曲线的焦点坐标F(5,0)F(5,0)F(0,5)F(0,5)F ( c, 0)F(0, c)确定焦点位置：椭圆看分母大小;双曲看系数正负！Evaluation only.Eval
13、uation 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 已知双曲线的焦点为F1(-5,0),F2(5,0)，双曲线上 一点P到F1、F2的距离的差的绝对值等于6，求双曲线 的标准方程. 2 2a a = 6,= 6, 2c=102
14、c=10 a a = 3, c = 5= 3, c = 5 b b2 2 = 5= 52 2- -3 32 2 =16=16所以所求双曲线的标准方程为：所以所求双曲线的标准方程为：根据双曲线的焦点在根据双曲线的焦点在 x x 轴上，设它的标准方程为轴上，设它的标准方程为 ：解:例题分析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.
15、0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.练习1 判断下列方程是否表示双曲线，若是，求出三量 的值（1） （2）（3）（4）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2:如果方程 表示双曲线，求m的取值范围.分析 :方程方程 表示双曲线时，则表示双曲线时，则mm的取值的取值范围范围_._.变式一:结论：结论：Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .
