pronhud:椭圆知识点详细总结

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椭圆方程式知识点总结 1. 椭圆方程的第一定义:

⑴①椭圆的标准方程: i. 中心在原点,焦点在 x 轴上: 上: ②一般方程: . .③椭圆的标准参数方程: 的参数方程 . ii. 中心在原点,焦点在 轴

为 (一象限 应是属于 ). ⑵①顶点: 或 .②轴:对称轴:x 轴, 轴;长轴长 长 或 .③焦点: .⑥离心率: 或 .④焦距: .⑦焦点半径: 上的一点,

,短轴

.⑤准线:

i. 设 为椭圆 右焦点,则 由椭圆方程的第二定义可以推出.

为左、

ii.设 为椭圆 上的一点, 由椭圆方程的第二定义可以推出. 由椭圆第二定义可知: 加右减”. 注意:椭圆参数方程的推导:得

为上、下焦点,则 归结起来为 “左

方程的轨迹为椭圆. 和 ,

⑧通径:垂直于 x 轴且过焦点的弦叫做通经.坐标: ⑶共离心率的椭圆系的方程:椭圆 的离心率是

方程 是大于 0 的参数, 离心率的椭圆系方程. ⑸若 P 是椭圆: 为 (用余弦定理与 上的点.

的离心率也是

我们称此方程为共

为焦点,若

,则

的面积 .

可得). 若是双曲线,则面积为

椭圆的简单几何性质

常见考法

在段考中,多以选择题、填空题和解答题的形式考查椭圆的简单几何性质。选择题和填空 题一般属于容易题,解答题一般属于难题。在高考中,一般以解答题的形式融合其它圆锥 曲线联合考查椭圆的几何性质,难度较大。 误区提醒 求椭圆的方程,用待定系数法,先定位,后定量。如果不能确定,要分类讨论。 【典型例题】


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