2021年高中数学解析几何椭圆性质及定义.pdf

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1、.-.word.zl-椭圆的性质及应用一、圆锥曲线圆锥与平面的截线通常有：圆、椭圆、双曲线、抛物线，其中的椭圆、双曲线、抛物线叫圆锥曲线，其中抛物线是圆锥面与平行于某条母线的平面相截而得的曲线，双曲线是圆锥面与平行于轴的平面相截而得的曲线，圆是圆锥面与垂直于轴的平面相截而得的曲线，其他平面截取的那么为椭圆。圆锥曲线有一个共同的定义：即：圆锥曲线是到定点距离与到定直线间距离之比为常值的点之轨迹。二、椭圆的定义椭圆是平面上到两定点的距离之和为常值的点之轨迹，也可定义为到定点距离与到定直线间距离之比为一个小于1 常值的点之轨迹。椭圆的第一定义：平面与两定点 F、F的距离的和等于常数2a(2a|FF|

2、)的动点 P的轨迹叫做椭圆。即：PF+PF=2a，其中两定点 F、F叫做椭圆的焦点，两焦点的距离FF叫做椭圆的焦距。假设2a=|FF|，为线段，假设 2ab0)，这样的椭圆长轴在x 轴上，焦点在X轴时，假设22221yxba，(ab0)，这样的椭圆长轴在y 轴上。焦点在y 轴时。有两条线段，a、b 中较大者为椭圆长半轴长，较短者为短半轴长，当ab 时，焦点在 x 轴上，焦距为222 ab，焦距与长、短半轴的关系:222acb椭圆的第二定义由椭圆的第一定义：可到椭圆方程为：2222222221bxabybyax将222cab代入，可得：22222222222222xacacxycaxacay所以

3、：22224222axaccxycaxaccxyP F F|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 1 页，共 9 页.-.word.zl-由此可得：accaxcxycaxaccxy22224222所以可得椭圆的第二个定义：平面上到定点 F 距离与到定直线间距离之比为常数的点的集合定点F 不在定直线上，该常数为小于 1 的正数,其中定点 F 为椭圆的焦点，定直线称为椭圆的准线该定直线的方程是2axc。常数 e是椭圆的离心率。(01)ceea注意：准线和焦点对应，左准线对应左焦点，右准线对应右焦点下面我们介绍第二定义的几何说明：可以找到两个球

4、，它们均满足：和圆锥相切于一个圆，与截面相切于一个点。一个在截面和圆锥顶角之间即截得的圆锥体的切球，小球，另一个在截面与圆锥顶角异侧即圆锥体外切球，大球。两个球与截面相切的两个点即是两个焦点，两个球与圆锥相切的两个圆，那两个圆所在的两个平面它们是平行的分别与原来的截面的交线即是两条准线。通过三角函数的知识应该可以证明截得的图形上的点到焦点和到相应准线的比值为定值|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 2 页，共 9 页文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 H

5、J9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1

6、HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1

7、 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R

8、1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1

9、R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F

10、1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9

11、F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6.-.word.zl-设 P 为截面与圆锥交线上的动点，两个球与截面的交点为固定点，即为椭圆的焦点，平面 与平面的交线为固定直线，即为椭圆的准线。E 为大球和截面的交点，显然 PP1为动点到定直

12、线的距离，设大的球心为 O，PE 和 PP2为大球外一点 P到大球的两个切线，所以有PE=PP2思考为什么 PE 一定为切线，PE 为截面 的直线，而截面与球仅仅一个交点椭圆的第三定义：椭圆的其他定义根据椭圆的一条重要性质也就是椭圆上的点与椭圆短轴两端点连线的斜率之积是定值 22ab可以得出：平面与两定点的连线的斜率之积是常数k 的动点的轨迹是椭圆，此时 k 应满足一定的条件，也就是排除斜率不存在的情况。三、.圆锥曲线的几何性质：1.椭圆 的面 积 是 ab。椭 圆 可 以看 作圆 在某 方 向 上的 拉伸，它 的 参 数方 程是：x=acos ，y=bsin 举例：假设Ryx,，且62322

13、yx，那么yx的最大值是 _，22yx的最小值是_答：5,22.标准形式为22221yxab的椭圆在 x0，y0点的切线为：00221xxyyab3.椭圆焦半径公式PF1=a+ex0 PF2=a-ex04.直线与椭圆位置关系1弦长公式：假设直线ykxb与圆锥曲线相交于两点A、B，且12,x x分别为 A、B 的横坐标，那么AB2121kxx，假设12,y y分别为 A、B 的纵坐标，那么AB21211yyk，2直线 l：y=x+1 与椭圆交于A，B 两点，P 为椭圆上一点，求PAB 面积的最大值.3相切、相交、相离的条件6直线与圆锥曲线的位置关系：1相交：0直线与椭圆相交；0直线与双曲线相交，

14、但直线与双曲线相交不一定有0，当直线与双曲线的渐近线平行时，直线与双曲线相交且只有一个交点，故0是直线与双曲线相交的充分条件，但不是必要条件；0直线与抛物线相交，但直线与抛物线相交不一定有0，当直线与抛物线的对称轴平行时，直线与抛物线相交且只有一个交点，故0也仅是直线与抛物线相交的充分条件，但不是必要条件。5围|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 3 页，共 9 页文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文

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16、文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L

17、6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5

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19、5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8

20、P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N

21、8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6.-.word.zl-即|x|a，|y|b，这说明椭圆在直线x=a和直线 y=b 所围成的矩形里(图 2-18)注意结合图形讲解，并指出描点画图时，就不能取围以外的点6对称性x 轴、y 轴是椭圆的对称轴，原点是椭圆的对称中心即椭圆中心7顶点只须令

22、 x=0，得 y=b，点 B1(0，-b)、B2(0，b)是椭圆和 y 轴的两个交点；令y=0，得x=a，点 A1(-a，0)、A2(a，0)是椭圆和 x 轴的两个交点强调指出：椭圆有四个顶点A1(-a，0)、A2(a，0)、B1(0，-b)、B2(0，b)8离心率教师直接给出椭圆的离心率的定义：再讲清离心率 e的几何意义：椭圆上一点到焦点的距离和它到准线的距离的比ac0，0e1再结合图形分析离心率的大小对椭圆形状的影响：(2)当 e接近 0 时，c 越接近 0，从而 b 越接近 a，因此椭圆接近圆；(3)当 e=0 时，c=0，a=b 两焦点重合，椭圆图形就是圆了课堂练习：1是椭圆上一点，假

23、设到椭圆右准线的距离是，那么到左焦点的距离为_|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 4 页，共 9 页文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:

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25、:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编

26、码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档

27、编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文

28、档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6

29、文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L

30、6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6.-.word.zl-2假设椭圆的离心率为，那么它的长半轴长是_答案：121 或 2 3求以下椭圆的长轴和短轴的长、焦距、离心率、各个顶点和焦点坐标、准线方程：(1)25x2+4y2-100=0，(2)x2+4y2-1=04我国发射的科学实验人造地球卫星的运行轨道是以地球的中心为一个焦点的椭圆，近地点距地面 266Km，远地点距地面 1826Km，求这颗卫星的轨道方程的方程 4答案：顶点(0，2)可能是长轴的端点，也可能是短轴的一个端点，故分两种情况求方程：5点 P 与一定点 F(2，0)的距离和它到一定直

31、线x=8 的距离的比是 12，求点 P 的轨迹方程，并说明轨迹是什么图形三、例题讲解例 1：求出椭圆方程13422yx和134)1(22yx长轴顶点、焦点、准线方程；解：因为把椭圆13422yx向右平移一个单位即可以得到椭圆134)1(22yx所以问题 1 中的所有问题均不变，均为21,1,3,3acecba13422yx长轴顶点、焦点、准线方程分别为：)0,2(，)0,1(4x；134)1(22yx长轴顶点、焦点、准线方程分别为：)0,12(，)0,11(14x；思考：求出椭圆方程14322yx准线方程|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载

32、.第 5 页，共 9 页文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6

33、 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D

34、6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10

35、D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N1

36、0D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N

37、10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10

38、N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6.-.word.zl-例 2、设 AB 是过椭圆

39、右焦点的弦，那么以AB 为直径的圆必与椭圆的右准线A.相切B.相离C.相交D.相交或相切分析：如何判断直线与圆的位置关系呢？解：设 AB 的中点为M，那么 M 即为圆心，直径是|AB|；记椭圆的右焦点为F，右准线为l；过点 A、B、M 分别作出准线l的垂线，分别记为ddd,21由梯形的中位线可知221ddd又由椭圆的第二定义可知edAF1|edBF2|即)(|21ddeBFAF又22|2|21ddeBFAFAB且10e2|ABd故直线与圆相离例 3、点 M 为椭圆1162522yx的上任意一点，1F、2F分别为左右焦点；且)2,1(A求|35|1MFMA的最小值求|1MFMA的最小值求|1MF

40、MA的最小值分析：应如何把|351MF表示出来解：左准线1l：3252cax，作1lMD于点 D，记|MDd由第二定义可知：53|1acedMF?dMF53|1?|351MFd故有|35|1MDMAdMAMFMA所以有当A、M、D 三点共线时，|MA|+|MD|有最小值：3251即|35|1MFMA的最小值是328变式 1：|5|31MFMA的最小值；解：283283)|35|(3|5|311MFMAMFMA变式 2：|531MFMA的最小值；解：52832853|)|35|(|53|5311MFMAMFMAD A F11M F21|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|

41、*|*|欢.|迎.|下.|载.第 6 页，共 9 页文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1

42、 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R

43、1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1

44、R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F

45、1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9

46、F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q

47、9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6.-.word.zl

48、-MAMFMFMAMFMA2211010|其最小值=10-AF2课堂练习：11216,)3,2(22yxFA是的右焦点，点 M 为椭圆的动点，求MFMA2的最小值，并求出此时点 M 的坐标。例 4.，为椭圆上的两点，是椭圆的右焦点假设，的中点到椭圆左准线的距离是，试确定椭圆的方程解：由椭圆方程可知、两准线间距离为设，到右准线距离分别为，由椭圆定义有，所以，那么，中点到右准线距离为，于是到左准线距离为，所求椭圆方程为例 5方程|2|)1()1(222yxyx表示什么曲线？解：222|2|)1()1(22yxyx122；即方程表示到定点的距离与到定直线的距离的比常数且该常数小于1方程表示椭圆例 6

49、、06高考 15如图把椭圆的长轴AB 分成 8 等分，过每个等分点作x轴的垂线交椭圆的上半局部于721,PPP七个点，F 是椭圆的一个焦点，那么|721FPFPFP=解法一：53ace，设iP的横坐标为ix，那么ixi455不妨设其焦点为左焦点|精.|品.|可.|编.|辑.|学.|习.|资.|料.*|*|*|*|欢.|迎.|下.|载.第 7 页，共 9 页文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10

50、S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC10S7N8P5L6文档编码:CW6R8Q9F1R1 HJ9P5A10N10D6 ZC1