[第八章第七节抛物线.ppt

返回 一、抛物线定义 平面内与一个定点F和一条定直线l(F?l)的距离 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 ． 相等的点 准线 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 二、抛物线的标准方程与几何性质 标准方程 图形 范围 对称轴 y2＝2px(p＞0) y2＝－2px(p＞0) x≥0，y∈R x≤0，y∈R x轴 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 顶点坐标 焦点坐标 准线方程 离心率 原点O(0,0) e＝1 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 标准方程 图形 范围 对称轴 x2＝ x2＝ 2py(p＞0) －2py(p＞0) y≥0，x∈R y≤0，x∈R y轴 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 顶点坐标 焦点坐标 准线方程 离心率 原点O(0,0) y＝ e＝1 y＝ Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 答案： C 解析：由条件知p＝1，即焦点到准线的距离为1. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 解析：由抛物线的定义知，点的轨迹是开口向左的抛物线，且p＝2，∴其方程为y2＝－2px＝－4x. 2．坐标平面内到定点F(－1,0)的距离和到定直线l：x＝1的距离相等的点的轨迹方程是 (　　) A．y2＝2x B．y2＝－2x C．y2＝4x D．y2＝－4x 答案： D Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 答案： B Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 答案：6 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 5．若抛物线的焦点在直线x－2y－4＝0上，则抛物线的标准方程是__________________． 解析：由x＝0，y＝－2，由y＝0，x＝4即(0，－2)或(4,0)为抛物线的焦点∴抛物线方程为y2＝16x或x2＝－8y. y2＝16x或x2＝－8y Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 1．抛物线定义中定点的要求 定点F不能在定直线l上，因为若定点F在定直线l上，则动点的轨迹为过点F且垂直于l的直线而非抛物线． 2．抛物线方程y2＝2px中，只有当p0时p有几何意义，且是抛物线的焦点到准线的距离． 3．由y2＝mx(m≠0)或x2＝my(m≠0)求焦点坐标时，只需 将x或y的系数除以4，