[椭圆的定义及性质.ppt

椭圆 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 一．椭圆的定义 平面内与两个定点F1、F2的距离之和等于常数2a（大于∣F1F2∣）的点的轨迹叫椭圆. 这两个定点F1、F2叫椭圆的焦点. 两焦点的距离∣F1F2∣叫椭圆的焦距（2c）. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1.动画演示 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 2.椭圆定义的符号表述： (2a2c) 注意： 1.当2a2c时,轨迹是椭圆 2.当2a=2c时,轨迹是一条线段, 是以 F1、F2为端点的线段． 3.当2a2c时,无轨迹,图形不存在. 4.当c=0时,轨迹为圆． Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二.椭圆的标准方程 (1)焦点在x轴 (2)焦点在y轴 看分母大小 1 2 y o F F P x 1 o F y x 2 F P Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 三.椭圆的几何性质 让我们一起研究标准方程为:标准方程为: 的椭圆的性质 的椭圆的性质 首先，我们有： 2a2c,a2=b2+c2, a0,b0,c0 2a2c,a2=b2+c2,a0,b0,c0 2a2c,a2=b2+c2,a0,b0,c0 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. F2 F1 x y 椭圆关于x轴、y轴、原点对称. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. O B1 A1 A2 y 可得x= ? a 在 中令y=0， 从而：A1(-a,0),A2(a,0) 同理：B1(0, -b),B2(0, b) A1 O B2 B1 A2 x y Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. O B2 B1 A1 A2 x y 线段A1A2叫椭圆的长轴: 线段B1B2叫椭圆的短轴: 长为2a 长为2b Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. F2 F1 O B2 B1 A1 A2 x y 横坐标的范围： 纵坐标的范围： -a? x ? a -b? y ? b 所以 由式子 知 从而：-a? x ? a Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 我们把两焦点F1、F2的距离叫椭圆的焦距 所以∣OF1∣= ∣OF2∣=c 因此 焦点F1 (-c