《椭圆的定义及性质》由会员分享，可在线阅读，更多相关《椭圆的定义及性质（22页珍藏版）》请在金锄头文库上搜索。
1、 椭圆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.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
2、焦点的距离F1F2叫椭圆的焦距（ 2c）.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.动画演示Evaluation only.Evaluation only. Created wi
3、th 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.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,a2=b2+c2, a0,b0,c02a2c,a2=b2+c2,a0,b
4、0,c0 2a2c,a2=b2+c2,a0,b0,c0 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.F2F1xy椭圆关于x轴、y轴、原点对称.Evaluation only.Evalu
5、ation 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.OB1A1A2y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)A1OB2B1A2xyEvaluation only.Ev
6、aluation 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.OB2B1A1A2 xy线段A1A2叫椭圆的长轴:线段B1B2叫椭圆的短轴:长为2a长为2bEvaluation only.Evaluation only. Created w
7、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.F2F1OB2B1A1A2 xy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 aEvaluation only.Evaluation only. Created with Aspose.
8、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.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,0)、 F2 (c,0) F1F2=2cEvaluation only.Evaluation only. Created with Aspose.Slide
9、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.Oxy把椭圆的焦距与长轴长的比叫作椭圆 的离心率，用e表示，即Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.C
10、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.Oxy所以 e(0，1) e越接近于0，椭圆越圆；e越接近于1，椭圆越扁.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NE
11、T 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.条件2a2c,a2=b2+c2,a0,b0,c0标标准方程图图形对对称性曲线线关于x轴轴、 y轴轴、原点对对称顶顶点长轴顶长轴顶 点(a,0) 短轴顶轴顶点(0,b)范围围焦点焦距离心率椭圆椭圆 的标标准方程及其简单简单 几何性质质(-c,0)和(c,0)(0,-c)和(0,c)曲线线关于x轴轴、 y轴轴、原点对对称长轴顶长轴顶 点(0,a) 短轴顶轴顶点(b,0)Evaluation only.
12、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.解析:B 基础自测由椭圆方程得 a=3, 由椭圆定义知所以P到另一个焦点的距离 为6-2=4.Evaluation only.Evaluation only. Create
13、d 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.D Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created wit
14、h Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.B 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.D 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 on
16、ly.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. =1. =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 2
