最详细的解析几何全解

1、1.近三年高考各试卷解析几何考查情况统计 2005年高考各地的16套试卷中，每套试卷均有1道解析几何解答题试题，涉及椭圆的有9道，涉及双曲线的有2道，涉及抛物线的有3道，涉及直线与圆的有3道，涉及线性规划的有1道.当中，求最值的有4道，求参数的取值范围的有4道，求轨迹方程的有5道，和向量综合的有7道，探索性的问题有5道. 2006年高考各地的18套试卷里，每套均有1道解答试题，涉及椭圆的有9道，抛物线的有4道，双曲线的有5道.当中求动点的轨迹，求参数的取值范围是热门话题.重庆的解析几何、数列、不等式证明相结合的试题比较独特.2007年高考各地的19套试卷中，每套均有1道解答题，椭圆的有8道，双

2、曲线的有4道，抛物线的3道，涉及到圆锥曲线中的最值问题、轨迹问题、中点弦问题等.解析几何解答试题热点的题型是求参数范围或求最值的综合性问题，探求动点的轨迹问题，有关定值、定点等的证明问题，与向量综合的探索性问题等.2.考查特点(1)由已知条件建立曲线的方程，研究曲线的性质.用待定系数法确定圆锥曲线的标准方程，求它们的焦点、焦距、准线、离心率等元素，研究几何性质.(2)直线与圆锥曲线的位置关系是高考重点考查内容之一，主要讨论直线和圆锥曲线的公共点问题，求弦长、焦点弦长及中点等问题.(3)有关解析几何的最值问题、曲线方程中含字母参数的范围问题以及对称问题是高考中经常出现的内容，涉及知识面广，常用到

3、函数、不等式和三角等方面的知识.(4)有关探索性题型，因为它具有考查思维能力、区分度较高的功能，所以经常结合其它章节的知识点出现在高考试题中.(5)平面向量和解析几何结合，已成为高考新的热点.(6)解析几何部分仍在考查基础知识的基础上，注重对数学思想方法的考查，注重对数学能力的考查，以逻辑思维能力为核心，全面考查其它各种能力，强调探索性、综合性，应用性，切合考生的实际，注重试题的层次性，合理调控综合程度，坚持多角度、多层次的考查.1.突出解析几何的基本思想 解析几何的实质是用代数方法研究几何问题，通过曲线的方程研究曲线的性质，因此要掌握求曲线方程的思路和方法，它是解析几何的核心之一.求曲线的方

4、程的常用方法有两类： 一类是曲线形状明确，方程形式已知(如直线、圆、圆锥曲线的标准方程等)，常用待定系数法求方程.另一类是曲线形状不明确或不便于用标准形式表示，一般采用以下方法：（1）直译法：将原题中由文字语言明确给出动点所满足的等量关系直接翻译成由动点坐标表示的等量关系式.（2）代入法：所求动点与已知动点有着相互关系，可用所求动点坐标（x,y）表示出已知动点的坐标，然后代入已知的曲线方程.（3）参数法：通过一个（或多个）中间变量的引入，使所求点的坐标之间的关系更容易确立，消去参数得坐标的直接关系便是普通方程.（4）交轨法：动点是两条动曲线的交点构成的，由x,y满足的两个动曲线方程中消去参数，

5、可得所求方程.故交轨法也属参数法.2.熟练掌握直线、圆、及圆锥曲线的基本知识 (1)直线和圆 直线的倾斜角及其斜率确定了直线的方向.需要注意的是： ()倾斜角的范围是：0；()所有的直线必有倾斜角，但未必有斜率. 直线方程的四种特殊形式，每一种形式都有各自成立的条件，应在不同的题设条件下灵活使用.如截距式不能表示平行于x轴、y轴以及过原点的直线，在求直线方程时尤其是要注意斜率不存在的情况. 讨论点与圆、直线与圆、圆与圆的位置关系时，一般可从代数特征(方程组解的个数)或几何特征(点或直线到圆心的距离与两圆的圆心距与半径的关系)去考虑，其中几何特征较为简捷、实用.(2)椭圆完整地理解椭圆的定义并重

6、视定义在解题中的应用.椭圆是平面内到两定点f1、f2的距离之和等于常数2a(2af1f2)的动点的轨迹.还有另一种定义（圆锥曲线的统一定义）：平面内到定点的距离和到定直线的距离之比为常数e(0e1)的动点轨迹为椭圆，（顺便指出：e1、e=1时的轨迹分别为双曲线和抛物线）.椭圆的标准方程有两种形式，决定于焦点所在的坐标轴.焦点是f（±c,0）时，标准方程为(ab0)；焦点是f（0，±c）时，标准方程为(ab0).这里隐含 a2=b2+c2，此关系体现在ofb(b为短轴端点)中.深刻理解a、b、c、e、的本质含义及相互关系，实际上就掌握了几何性质.(3)双曲线 类比椭圆，双曲线

7、也有两种定义，两种标准方程形式.同样要重视定义在解题中的运用，要深刻理解几何量a、b、c、e、的本质含义及其相互间的关系. 双曲线的渐近线是区别于椭圆的一道“风景线”，其实它是矩形的两条对角线所在的直线（参照课本）. 双曲线(a0,b0)隐含了一个附加公式c2=a2+b2.此关系体现在oab(a,b分别为实轴,虚轴的一个端点)中；特别地，当a=b时的双曲线称为等轴（边）双曲线，其离心率为 .(4)抛物线抛物线的定义：平面内到一个定点f和一条定直线l的距离相等的点的轨迹（f l）.定义指明了抛物线上的点到焦点与准线的距离相等，并在解题中有突出的运用.抛物线方程（标准）有四种形式：y2=±

8、;2px和x2=±2py(p0)，选择时必须判定开口与对称轴.掌握几何性质，注意分清2p,p, 的几何意义.3.掌握直线与圆锥曲线的位置关系的研究方法(1)判断直线l与圆锥曲线c的位置关系，可将直线l的方程代入曲线c的方程，消去y(也可以消去x)得到一个关于变量x的一元方程ax2+bx+c=0，然后利用“”法.(2)有关弦长问题，应用弦长公式及韦达定理，设而不求;有关焦点弦长问题，要重视圆锥曲线的定义的运用，以简化运算.(3)有关弦的中点问题，除了利用韦达定理外，要注意灵活运用“点差法”，设而不求，简化运算.(4)有关垂直关系问题，应注意运用斜率关系(或向量方法)及韦达定理，设而不求

9、，整体处理.(5)有关圆锥曲线关于直线l的对称问题中，若a、a是对称点，则应抓住aa的中点在l上及ka a· kl=1这两个关键条件解决问题.(6)有关直线与圆锥曲线的位置关系中的存在性问题，一般采用“假设反证法”或“假设验证法”来解决.1.（北京清华大学附中模拟题）无论m为任何实数，直线l:y=x+m与双曲线c: (b0)恒有公共点.（）求双曲线c的离心率e的取值范围；（）若直线l过双曲线c的右焦点f，与双曲线交于p，q两点，并且满足，求双曲线c的方程.点评 第1问的解答方法较多，可以转化为求与抛物线相切的直线，也可以利用判别式法来求，还可以利用点到直线的距离转化为函数求最值.第2

10、问要证明平行于ab的弦被定直线平分，只需说明弦的中点的恒定性，这是一种转化的思想.9jwkffwvg#tym*jg&6a*cz7h$dq8kqqfhvzfedswsyxty#&qa9wkxfyeq!djs#xuyup2knxpr89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxg89amue9aqgn8xp$r#&#849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazad

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32、n&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9we

33、wz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89a

34、mv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$v

35、stt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&am

36、p;qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#

37、kn&muwfa5uxy7jnd6ywrrwwcvr9&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z

38、89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amyw

39、pazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9

40、cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv3tngk8!z89amywpazadnu#kn&muwfa5u

41、xy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&

42、amp;gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qc

43、ue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mzadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&a

44、mp;gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5

45、pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amyw

46、v*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8

47、!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6yw

48、rrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&

49、amp;muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89a

50、mywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#q

51、cue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4

52、ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vst

53、t#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqvue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7

54、jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9we

55、wz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89a

56、mywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849

57、gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr

58、9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp

59、$vstt#&ksv*3tngk8!z89amywpazadnugk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#

60、kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&m

61、uwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv84!z89amv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&

62、amp;gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$ue9wewz#qcue%&qypeh5pdx2zvkum&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9cpbk!zn%mz849gxgjqv$u*3tngk8!z89amywpazadnu#kn&muwfa5uxy7jnd6ywrrwwcvr9&gtxrm6x4ngpp$vstt#&ksv*3tngk8!z89amywpazadnu#kn&muwfa5uxy7