第九章解析几何9.7抛物线理INCLUDEPICTURE"\\\\程亚杰\\e\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"\\\\程亚杰\\e\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\数学人教版\\word\\基础知识自主学习.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\马玉娜\\马玉娜\\2017\\大一轮\\大一轮一校\\数学人教\\程亚杰\\word\\基础知识自主学习.TIF"\*MERGEFORMATINET1．抛物线的概念平面内与一个定点F和一条定直线l(l不经过点F)的距离相等的点的轨迹叫做抛物线．点F叫做抛物线的焦点，直线l叫做抛物线的准线．2．抛物线的标准方程与几何性质标准方程y2＝2px(p>0)y2＝－2px(p>0)x2＝2py(p>0)x2＝－2py(p>0)p的几何意义：焦点F到准线l的距离图形INCLUDEPICTURE"\\\\程亚杰\\e\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"\\\\程亚杰\\e\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINET1INCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE2"E:\\程亚杰\\2017\\一轮\\数学\\原WORD\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\程亚杰\\2017\\一轮\\数学\\数学人教版\\word\\9-42.TIF"\*MERGEFORMATINETINCLUDEPICTURE"E:\\马玉娜\\马玉娜\\2017\\大一轮\\大一轮一校\\数学人教\\程亚杰\\word\\9-42.TIF"\*MERGEFORMATINET顶点O(0,0)对称轴y＝0x＝0焦点FFFF离心率e＝1准线方程x＝－x＝y＝－y＝范围x≥0，y∈Rx≤0，y∈Ry≥0，x∈Ry≤0，x∈R开口方向向右向左向上向下【知识拓展】1．抛物线y2＝2px(p>0)上一点P(x0，y0)到焦点F的距离|PF|＝x0＋，也称为抛物线的焦半径．2．y2＝ax的焦点坐标为，准线方程为x＝－.3．设AB是过抛物线y2＝2px(p>0)焦点F的弦，若A(x1，y1)，B(x2，y2)，则(1)x1x2＝，y1y2＝－p2.(2)弦长|AB|＝x1＋x2＋p＝(α为弦AB的倾斜角)．3(3)以弦AB为直径的圆与准线相切．(4)通径：过焦点垂直于对称轴的弦，长等于2p，通径是过焦点最短的弦．【思考辨析】判断下列结论是否正确(请在括号中打“√”或“×”)(1)平面内与一个定点F和一条定直线l的距离相等的点的轨迹一定是抛物线．(×)(2)方程y＝ax2(a≠0)表示的曲线是焦点在x轴上的抛物线，且其焦点坐标是(，0)，准线方程是x＝－.(×)(3)抛物线既是中心对称图形，又是轴对称图形．(×)(4)AB为抛物线y2＝2px(p>0)的过焦点F(，0)的弦，若A(x1，y1)，B(x2，y2)，则x1x2＝，y1y2＝－p2，弦长|AB|＝x1＋x2＋p.(√)1．(2016·四川)抛物线y2＝4x的焦点坐标是()A．(0,2)B．(0,1)C．(2,0)D．(1,0)答案D解析 对于抛物线y2＝ax，其焦点坐标为，∴对于y2＝4x，焦点坐标为(1,0)．2．(2016·甘肃张掖...
