(完整word版)高中抛物线知识点归纳总结与练习题及答案(word文档良心出品).pdf

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1、抛物线专题复习知识点梳理：抛物线)0(22ppxy)0(22ppxy)0(22ppyx)0(22ppyx定义平面内与一个定点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。MFM=点 M到直线 l 的距离 范围0,xyR0,xyR,0 xR y,0 xR y对称性关于x轴对称关于y轴对称焦点(2p,0)(2p,0)(0,2p)(0,2p)焦点在对称轴上顶点(0,0)O离心率e=1 准线方程2px2px2py2py准线与焦点位于顶点两侧且到顶点的距离相等。顶点到准线的距离2p焦点到准线的距离p焦半径11(,)A xy12pAFx12pAFx12

2、pAFy12pAFyx y O l F x y O l F l F x y O x y O l F 焦 点弦长AB12()xxp12()xxp12()yyp12()yyp焦点弦AB 的几条性质11(,)A x y22(,)B xy以AB为直径的圆必与准线 l 相切若AB的倾斜角为，则22sinpAB若AB的倾斜角为，则22cospAB2124px x212y yp112AFBFABAFBFAFBFAFBFp切线方程00()y yp xx00()y yp xx00()x xp yy00()x xp yy一直线与抛物线的位置关系直线，抛物线，消 y 得：（1）当 k=0 时，直线 l 与抛物线的对

3、称轴平行，有一个交点；（2）当 k0 时，0，直线 l 与抛物线相交，两个不同交点；=0，直线 l 与抛物线相切，一个切点；0，直线 l 与抛物线相离，无公共点。（3）若直线与抛物线只有一个公共点,则直线与抛物线必相切吗?（不一定）二关于直线与抛物线的位置关系问题常用处理方法直线 l：bkxy抛物线，)0(p联立方程法：pxybkxy220)(2222bxpkbxkox 22,B xyFy11,A x y文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A

4、3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10

5、A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX1

6、0A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX

7、10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:C

8、X10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:

9、CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码

10、:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4设 交 点 坐 标 为),(11yxA,),(22yxB，则 有0,以 及2121,xxxx，还 可 进 一 步 求 出bxxkbkxbkxyy2)(212121，2212122121)()(bxxkbxxkbkxbkxyy在涉及弦长，中点，对称，面积等问题时，常

11、用此法，比如相交弦 AB的弦长2122122124)(11xxxxkxxkABak21或2122122124)(1111yyyykyykABak21抛物线练习1、已知点 P 在抛物线y2=4x 上，那么点P 到点 Q（2，1）的距离与点P 到抛物线焦点距离之和取得最小值时，点 P 的坐标为2、已知点P是抛物线22yx上的一个动点，则点P到点（0，2）的距离与P 到该抛物线准线的距离之和的最小值为3、直线3yx与抛物线24yx交于,A B两点，过,A B两点向抛物线的准线作垂线，垂足分别为,P Q，则梯形APQB的面积为4、设O是坐标原点，F是抛物线22(0)ypx p的焦点，A是抛物线上的一点

12、，FA与x轴正向的夹角为60，则OA为5、抛物线24yx的焦点为F，准线为l，经过F且斜率为3的直线与抛物线在x轴上方的部分相交于点A，AKl，垂足为K，则AKF的面积是6、已知抛物线2:8Cyx的焦点为F，准线与x轴的交点为K，点A在C上且2AKAF，则AFK的面积为7、已知双曲线22145xy，则以双曲线中心为焦点，以双曲线左焦点为顶点的抛物线方程为8、在平面直角坐标系xoy中，有一定点(2,1)A,若线段OA的垂直平分线过抛物线22(0)ypx p则该抛物线的方程是。9、在平面直角坐标系xoy中，已知抛物线关于x轴对称，顶点在原点O，且过点 P(2，4)，则该抛物线的方程是10、抛物线2

13、yx上的点到直线4380 xy距离的最小值是11、已知抛物线y2=4x,过点 P(4,0)的直线与抛物线相交于A(x1,y1),B(x2,y2)两点，则y12+y22的最小值是12、已知点11(,)A x y,22(,)B xy12(0)x x是抛物线22(0)ypx p上的两个动点,O是坐标原点,向量文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7

14、HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7

15、 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X

16、7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10

17、X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C1

18、0X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C

19、10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8

20、C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4OA,OB满足OAOBOAOB.设圆C的方程为221212()()0 xyxxxyyy。(1)证明线段AB是圆C的直径;(2)当圆 C 的圆心到直线x-2y=0 的距离的最小值为2 55时，求 p 的值。解：(1)证明:22,()()OAOBOAOBOAOBOAOB，222222OAOA OBOBOAOA OBOB，整理得:0OA OB，12120 xxyy(1)以

21、线段 AB 为直径的圆的方程为2222121212121()()()()224xxyyxyxxyy，展开并将(1)代入得:221212()()0 xyxxxyyy，故线段AB是圆C的直径(2)解:设圆 C 的圆心为 C(x,y),则121222xxxyyy圆心 C 到直线 x-2y=0 的距离为d,则1212|()|25xxyyd2211222,2(0)ypxypxp，22121224y yx xp，又因12120 xxyy，1212xxyy，22121224y yyyp，12120,0 xxyy，2124yyp，2212122221212121|()()|24()8|454 5yyyyyyy

22、 yp yyppdp2212(2)44 5yyppp，当122yyp时,d 有最小值5p,由题设得2 555p，2p.13、已知正三角形OAB的三个顶点都在抛物线22yx上，其中O为坐标原点，设圆C是OAB的内接圆（点C为圆心）（1）求圆C的方程；（2）设圆M的方程为22(47cos)(7cos)1xy，过圆M上任意一点P分别作圆C的两条切线文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N

23、4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2

24、N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y

25、2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2

26、Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X

27、2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5

28、X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y

29、5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4PEPF，切点为EF，求CE CF，的最大值和最小值（1）解：设AB，两点坐标分别为11()xy，22()xy，由题设知22221122xyxy又因为2112yx，2222yx，可得22112222xxxx即1212()(2)0 xxxx由10 x，20 x，可知12xx，故AB，两点关于x轴对称，所以圆心C在x轴上设C点的坐

30、标为(0)r，则A点坐标为3322rr，于是有233222rr，解得4r，所以圆C的方程为22(4)16xy（2）解：设2ECFa，则2|cos216cos 232cos16CE CFCECF在RtPCE中，4cos|xPCPC，由圆的几何性质得|17PCMC18，|1716PCMC，所以12cos23，由此可得1689CE CF则CE CF的最大值为169，最小值为814、如图，已知点(10)F，直线:1lx，P为平面上的动点，过P作直线l的垂线，垂足为点Q，且QP QFFP FQ（1）求动点P的轨迹C的方程；（2）过点F的直线交轨迹C于AB，两点，交直线l于点M，已知1MAAF，12MBB

31、F，求12的值；解：（1）设点()P xy，则(1)Qy，由QP QFFP FQ得：(1 0)(2)(1)(2)xyxyy，化简得2:4Cyx（2）设直线AB的方程为1(0)xmym设11()A xy，22()B xy，又21Mm，联立方程组241yxxmy，消去x得：2440ymy，2(4)120m，故121244yymy y，O y x 1 l F P B Q M F O A x y 文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7

32、 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X

33、7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10

34、X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C1

35、0X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C

36、10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8

37、C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B

38、8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4由1MAAF，2MBBF得：1112yym，2222yym，整理得：1121my，2221my，12122112myy121222yymy y2 424mm0文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7

39、 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X

40、7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10

41、X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C1

42、0X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C

43、10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8

44、C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4文档编码:CX10A3B8C10X7 HF10R1E7I8Z8 ZK1Y5X2Y2N4