抛物线的几何性质-抛物线焦点弦的性质复习过程.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,2.4.2,抛物线的几何性质,抛物线焦点弦的性质,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,1.,抛物线,y,2,2px,（,p,0,）的范围、对称性、顶点、离心率、焦半径分别是什么？,范围：,x0,，,yR,；,对称性：关于,x,轴对称；,顶点：原点；,离心率：,e,1,；,焦半径：,.,复习回顾,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,过抛物线的焦点,F,作直线交抛物线于,A,、,B,两点，线段,AB,叫做,抛物线的焦点弦,，请你探究焦点弦具有哪些性质,.,O,x,y,B,A,F,问题提出,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,1,、焦点弦,AB,的长如何计算？,设,AB,为,焦点弦,.,点,A(x,1,，,y,1,),，,B(x,2,，,y,2,),|AB|,x,1,x,2,p,O,x,y,B,A,F,探求新知,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,2,、抛物线的焦点弦,AB,的长是否存在最小值？若存在，其最小值为多少？,垂直于对称轴的焦点弦最短，叫做抛物线的,通径,，其长度为,2p,O,x,y,B,A,F,探求新知,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,3,、,A,、,B,两点的坐标是否存在相关关系？若存在，其坐标之间的关系如何？,O,x,y,B,A,F,探求新知,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,4,、利用焦半径公式，,|AF|,|BF|,可作哪些变形？,|AF|,与,|BF|,之间存在什么内在联系？,O,x,y,B,A,F,探求新知,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,O,x,y,B,A,F,5,、由焦点弦长公式,得 ，,这个等式的几何意义是什么？,以,AB,为直径的圆与,抛物线的准线相切,.,探求新知,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,6,、设点,M,为抛物线准线与,x,轴的交点，则,AMF,与,BMF,的大小关如何？,相等,C,D,O,x,y,B,A,F,M,探求新知,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,7,、过点,A,、,B,作准线的垂线，垂足分别为,C,、,D,，则,ACF,和,BDF,都是等腰三角形，那么,CFD,的大小如何？,90,C,D,O,x,y,B,A,F,探求新知,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,过抛物线,y,2,=2px,的焦点,F,作直线交抛物线于,A,、,B,两点，焦点弦,AB,具有如下性质,.,形成结论,O,B,A,F,C,x,y,D,M,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,例,1,过抛物线焦点,F,的直线交抛物线于,A,、,B,两点，过点,A,和抛物线顶点的直线交抛物线的准线于点,C,，求证：直线,BC,平行于抛物线的对称轴,.,O,B,A,F,C,x,y,例题讲解,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,O,B,A,F,C,x,y,例题讲解,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,例题讲解,O,B,A,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,B,A,x,y,例题讲解,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,例题讲解,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,课堂小结,1.,抛物线有许多几何性质，探究抛物线的几何性质，可作为一个研究性学习课题，其中焦点弦性质中的有些结论会对解题有一定的帮助,.,2.,焦点弦性质,y,1,y,2,p,2,是对焦点在,x,轴上的抛物线而言的，对焦点在,y,轴上的抛物线，类似地有,x,1,x,2,p,2,.,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,