抛物线焦点弦性质(1)演示教学.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,*,*,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,*,*,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,*,*,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,*,*,抛物线焦点弦性质,永城市高级中学 邵锋,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,1、通径：,通过焦点且垂直对称轴的直线，,与抛物线相交于两点，连接这,两点的线段叫做抛物线的,通径,。,x,O,y,F,P,通径的长度,：2P,2、焦半径：,连接抛物线任意一点与焦点的线段叫做抛物线的,焦半径,。,一 定义,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,通过焦点的直线，与抛物,线相交于两点，连接这两点的,线段叫做抛物线的,焦点弦,。,x,O,y,F,A,3.焦点弦：,B,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,方程,图,形,范围,对称性,顶点,焦半径,焦点弦的长度,y,2,=2,px,（,p,0）,y,2,=-2,px,（,p,0）,x,2,=2,py,（,p,0）,x,2,=-2,py,（,p,0）,l,F,y,x,O,l,F,y,x,O,l,F,y,x,O,x,0,y,R,x,0,y,R,x,R,y,0,y,0,x,R,l,F,y,x,O,关于x轴对称,关于x轴对称,关于y轴对称,关于y轴对称,（0,0）,（0,0）,（0,0）,（0,0）,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,A,F,B,证明,？,课本P119习题,8.5的第7题,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,引申,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,A,F,B,分析,结论,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,A,F,B,分析,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,【探究】过焦点的所有弦中，何时最短？,【,结论,】过焦点的弦中通径长最小。,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 的焦点作直线交抛物线于,两点若 ，则|AB|=_,过抛物线 的焦点作倾斜角为 的弦，则此弦长,为_；一条焦点弦长为16，则弦所在的直线倾斜,角为 _,过抛物线 的对称轴上有一点M(p,0)，,作一条直线与抛物线交于A、B两点，若A点纵坐标为,，则B点纵坐标为 _,例题,8,24,4p,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,【探究1】以AB为直径的圆与抛物线的准线的位置关系？,设M为AB的中点,过A点作准线的垂线AA1,过B点作准线的,垂线BB1,过M点作准线的垂线MM1，由梯形的中位线性质和抛物线的定义知:,【,结论1,】以AB为直径的圆与抛物线的准线相切。,x,y,M,O,F,B,A,A1,B1,M1,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,【探究2】连接A,1,F、B,1,F 则 A,1,F、B,1,F有什么关系？,【探究3】弦端点A、B与原点连线的直线斜率之积等于定值-4.,【,结论3,】,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,【探究4】A,O,B,1,三点是否共线?,【结论4】A,O,B,1,三点共线,。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,x,O,y,F,A,B,【探究5】,是否为定值？,【结论5】,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,【探究6】抛物线焦点弦的端点A,B为切点的两条切线,是否相互垂直？,【结论6】抛物线焦点弦的端点A,B为切点的两条切线相互垂直。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,例题,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,例题2,过抛物线 的焦点F作一直线交抛物线于P、Q两点，若,PF与FQ的长分别是,()(A)2a (B)(C)4a(D),y,x,F,.,P,Q,C,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,小结,本节课，我们主要从代数（方程）的角度和几何观点,研究抛物线的焦点弦的一些性质。而对于从几何观点,去研究它的性质，希望同学们课后进一步的完成。,Evaluation only.,Created with Aspose.Slides for.NET 3.5 Client Profile 5.2.0.0.,Copyright 2004-2011 Aspose Pty Ltd.,