2022年高中数学平面解析几何初步经典例题 .pdf

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1、etters and calls, and do practical things for the masses combine good, effective through rea ching pe opl e at the service of the last mile. Third, foster the development of new energy, new Ge neral Secretary XI Jinping stressed development of innovation forest restructuring, revitalization of the o

2、ld industrial bases in Northeast China is the States major strategy, Central has issue d comprehensive opinions of revitalizing Northeast Chi na and other old ind ustrial bases, the CPC Central Committee on revitalization in Northeast China were . Vigorous determination does not waver, the work does

3、 not slacken off. Be firm with in the development has more to do with hard, and not muddle along, passive inaction. To rely on their own efforts, cant wait, cant wait, stand still. This not only provides new opportunities for developme nt in our region, and gave us new requirements. We must seize th

4、e opportunity, full use of national poli cy, has to be more complicated, to start and target, give full play to the initiative of leading cadres at all levels, active, active, focusing on building new momentum for development, accelerating transformation of forest developme nt. To implement the new

5、development philosophy. Philosophy is the action guide, new ideas and new developments. Carrying out innovation, coor dination and development of green, open, shared ideas, must be measurable, direct action with new development concepts, training cadres. In a new development concept as a yardstick.

6、Established in line with the new concept of evaluation system and evaluation criteri on, embodies the new development policy, organization, mandate implementation, always measured by the new development philosophy, continuous correction of forest transition course. In a new development concept for t

7、he path command. As part of the implementation of the new developme nt philosophy followed and action guideli nes, firmly adjusted, corre cted and reject unsuitable, ina ppr opriate and even against the new development ideas, behaviors and practices, more pragmatic approach based on a broad vision,

8、a nd creatively carry out ecological construction, industrial developme nt, improving pe ople s livelihood, such as the work to ensure that new development ideas take root in forest areas. In a new development concept for weapon training ca dre. Education leaders in the new, nothing two articles, en

9、ha nci ng vitality and power. Combined development six big industry, and implementation three big engineering, and create two big environment, strengthening on new development, and new economy concept of learning, and grasp and usi ng, real put thought and action unified to new development concept u

10、p, at with new development concept armed himself, and guide practice, effective do adv ocate innovation, and focused on coordination, a nd advocate green, a nd thick plant open, and adva nce shared. Second, we must rely on Science and technology affects. echni cal innovation is the promotion of econ

11、omic transformation and upgrading, quality and efficie ncy first power. ivelihood, i s related to peoples well-being and social harmony and stability. We need to protect and improve the livelihood of the people as the starting point and ending poi nt of transition and improve forest peoples feeling

12、and happiness. To promote poverty relief and development work. Implementing poverty alleviation crucial project is a major strategic decision made by the CPC Central Committee, is also determined by the provi ncial first project, we must unify thinking and action to the requirements of the Central,

13、provincial, resolutely win the poverty battle. The previous pha se I to 18 stations, Tahe, Pine Ridge research, visited many of the poor, go, the heavier, more pressure. For poverty relief and development work, we must pay attention to it, always in mind, grasping ha nds, should not be blindly optim

14、istic, there can be no slack. Poverty alleviation and development lies in precise, accurate. Present, in order to find out the real base of poor people as soon as possi ble, come up with feasible poverty standards, state card, built on the basis of document management. To firmly establish the povert

15、y reduction concept, increase the intensity of resource integration, and related funding, with limited funds wisely. By using a combination of employment, entreprene urship for poverty eradication poverty eradication, education, poverty alleviation, medical aid of poverty means, due to effects of po

16、licies, those policies, ensure the completion of mission obje ctives for poverty eradication for the year. To actively promote the construction of new towns. In February this year, promulgated by the State Council on further promoting urbanizati on construction of new opi nions, proposed to adhere t

17、o the people-centered, four modernizations synchronization, optimization, ecol ogy civilization and cultural heritage of new urbanization path with Chi nese chara cteristics. According to district -wide construction of civilized city and the beautiful countryside, further strengthe ning of urban tra

18、nsport, water supply and drainage and sew age, waste disposal ground, underground, such as infrastructure construction, strive to create a safer and more livable environment. To actively seize the full stop and opportunities for poverty alleviation and development, further efforts to increa se fores

19、t villages merge, population to the County (district) Council sites and centres concentrated in villages and towns. Combined development of urban construction and tourism industries, careful planni ng and constructi on of a number of suitable for residential and farm tour towns and villages, forming

20、 one village one product, a feature pattern. Closer to the masses. Since last year, our in-de pth implementation of the leading cadres of grassroots masses at work, solve the pr oblems of a large number of people, get the masses give whol ehearted support to and praise, this work will carry on, abso

21、lutely cannot or movement. Grassroots masses and cadres in combination with poverty reduction, combined with the steady work of直线和圆的方程一、知识导学1两点间的距离公式: 不论A(x1，y1) ，B(x2，y2) 在坐标平面上什么位置，都有d=|AB|=221221)()(yyxx，特别地，与坐标轴平行的线段的长|AB|=|x2x1| 或|AB|=|y2-y1|. 2定比分点公式: 定比分点公式是解决共线三点A(x1，y1) ，B(x2，y2) ，P(x，y)之间数

22、量关系的一个公式，其中 的值是起点到分点与分点到终点的有向线段的数量之比.这里起点、分点、终点的位置是可以任意选择的，一旦选定后的值也就随之确定了. 若以A为起点， B为终点， P为分点，则定比分点公式是112121yyyxxx. 当 P点为 AB的中点时，=1，此时中点坐标公式是222121yyyxxx. 3直线的倾斜角和斜率的关系（1）每一条直线都有倾斜角，但不一定有斜率. （2）斜率存在的直线，其斜率k与倾斜角 之间的关系是k=tan . 4确定直线方程需要有两个互相独立的条件。直线方程的形式很多，但必须注意各种形式的直线方程的适用范围. 名称方程说明适用条件斜截式bkxyk为直线的斜率

23、b 为直线的纵截距倾斜角为90的直线不能用此式点斜式)(00 xxkyy(00,yx) 为直线上的已知点，k为直线的斜率倾斜角为90的直线不能用此式两点式121yyyy=121xxxx(11, yx) ，(22, yx) 是直线上两个已知点与两坐标轴平行的直线不能用此式截距式ax+by=1 a为直线的横截距b 为直线的纵截距过（ 0，0）及与两坐标轴平行的直线不能用此式一般式0CByAxBA，AC，BC分别为斜率、横截距和纵截距A、B不全为零5 两条直线的夹角。 当两直线的斜率1k,2k都存在且1k2k -1 时， tan =21121kkkk，当直线的斜率不存在时，可结合图形判断. 另外还应

24、注意到： “到角”公式与“夹角”公式的精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 8 页区别 . 6怎么判断两直线是否平行或垂直？判断两直线是否平行或垂直时，若两直线的斜率都存在， 可以用斜率的关系来判断；若直线的斜率不存在，则必须用一般式的平行垂直条件来判断 . （1）斜率存在且不重合的两条直线l111bxky，l222bxky，有以下结论：l1l21k=2k，且12l1l21k2k= -1 （2）对于直线l10111CyBxA，l20222CyBxA，当A1，A2，B1，B2都不为零时，有以下结论：l1l221AA=21BB21

25、CCl1l2A1A2+B1B2 = 0 l1与l2相交21AA21BBl1与l2重合21AA=21BB=21CC7点到直线的距离公式. （1）已知一点P（00,yx）及一条直线l：0CByAx，则点 P 到直线l的距离d=2200|BACByAx；（ 2 ） 两 平 行 直 线l1:01CByAx，l2:02CByAx之 间 的 距 离d=2221|BACC. 8确定圆方程需要有三个互相独立的条件。圆的方程有两种形式，要知道两种形式之间的相互转化及相互联系（1）圆的标准方程：222)()(rbyax，其中（a，b）是圆心坐标，r是圆的半径；（2）圆的一般方程：022FEyDxyx（FED422

26、 0） ，圆心坐标为（ -2D，-2E） ，半径为r=2422FED. 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 8 页etters and calls, and do practical things for the masses combine good, effective through reaching pe opl e at the service of the last mile. Third, foster the development of new energy, new Ge neral Secretary

27、XI Jinping stressed development of innovation forest restructuring, revitalization of the old industrial bases in Northeast China is the States major strategy, Central has issue d comprehensive opinions of revitalizing Northeast Chi na and other old industrial bases, the CPC Central Committee on rev

28、italization in Northeast China were . Vigorous determination does not waver, the work does not sla cken off. Be firm with in the development has more to do with hard, and not muddle along, passive inaction. To rely on their own efforts, cant wait, cant wait, stand still. This not only provides new o

29、pportunities for developme nt in our region, and gave us new requirements. We must seize the opportunity, full use of national poli cy, has to be more complicated, to start and target, give full play to the initiative of leading cadres at all levels, active, active, focusing on building new momentum

30、 for development, accelerating transformation of forest developme nt. To implement the new development philosophy. Philosophy is the action guide, new ideas and new developments. Carrying out innovation, coor dination and development of green, open, shared ideas, must be measurable, direct action wi

31、th new development concepts, training cadres. In a new development concept as a yardstick. Established in line with the new concept of evaluation system and evaluation criteri on, embodies the new development policy, organization, mandate implementation, always measured by the new development philos

32、ophy, continuous correction of forest transition course. In a new development concept for the path command. As part of the implementation of the new developme nt philosophy followed and action guideli nes, firmly adjusted, corre cted and reject unsuitable, ina ppr opriate and even against the new de

33、velopment ideas, behaviors and practices, more pragmatic approach based on a broad vision, a nd creatively carry out ecological construction, industrial developme nt, improving pe ople s livelihood, such as the work to ensure that new development ideas take root in forest areas. In a new development

34、 concept for weapon training ca dre. Education leaders in the new, nothing two articles, enha nci ng vitality and power. Combined development six big industry, and implementation three big engineering, and create two big environment, strengthening on new development, and new economy concept of learn

35、ing, and grasp and usi ng, real put thought and action unified to new development concept up, at with new development concept armed himself, and guide practice, effective do advocate innovation, and focused on coordination, a nd advocate green, a nd thick plant open, and adva nce shared. Second, we

36、must rely on Science and technology affects. echni cal innovation is the promotion of economic transformation and upgrading, quality and efficie ncy first power. ivelihood, is related to peoples well-being and social harmony and stability. We need to protect and improve the livelihood of the people

37、as the starting point and ending poi nt of transition and improve forest peoples feeling and happiness. To promote poverty relief and devel opment work. Implementing poverty alleviation crucial project is a major strategic decision made by the CPC Central Committee, is also determined by the provinc

38、ial first project, we must unify thinking and action to the requirements of the Ce ntral, provincial, resolutely win the poverty battle. The previous phase I to 18 stations, Tahe, Pine Ridge research, visited many of the poor, go, the heavier, more pressure. For poverty relief and development work,

39、we must pay attention to it, always in mind, grasping ha nds, should not be blindly optimistic, there can be no slack. Poverty alleviation and development lies in precise, accurate. Present, in order to find out the real base of poor people as soon as possi ble, come up with feasible poverty standar

40、ds, state card, built on the basis of document management. To firmly establish the poverty reduction concept, increase the intensity of resource integration, and related funding, with limited funds wisely. By using a combination of employment, entrepreneurship for poverty eradication poverty eradica

41、ti on, education, poverty alleviation, medical aid of poverty means, due to effects of policies, those policies, ensure the completion of mission objectives for poverty eradication for the year. To actively promote the construction of new towns. In February this year, promulgated by the State Counci

42、l on further promoting ur banization construction of new opi nions, proposed to adhere to the people-centered, four modernizations synchronization, optimization, ecol ogy civilization and cultural heritage of new urbanization path with Chi nese characteristics. According to district-wide constructio

43、n of civilized city and the beautiful countryside, further strengthening of urban transport, water supply and drainage and sew age, waste disposal ground, underground, such as infrastructure construction, strive to create a safer and more livable environment. To actively seize the full stop and oppo

44、rtunities for poverty alleviation and development, further efforts to increase forest villages merge, population to the County (district) Council sites and centres concentrated in villages and towns. Combined development of urban construction and tourism industries, careful planni ng and constructio

45、n of a number of suitable for residential and farm tour towns and villages, forming one village on e product, a feature pattern. Closer to the masses. Since last year, our in-de pth implementation of the leading cadres of grassroots masses at work, solve the pr oblems of a large number of people, ge

46、t the masses give whol ehearted support to and praise, this work will carry on, absolutely cannot or movement. Grassroots masses and cadres in combination with poverty reduction, combined with the steady work of3 二、疑难知识导析1直线与圆的位置关系的判定方法. （1）方法一直线：0CByAx；圆：022FEyDxyx. 0022FEyDxyxCByAx消元一元二次方程acb42判别式

47、相离相切相交000（2）方法二直线:0CByAx；圆：222)()(rbyax，圆心（a，b）到直线的距离为d=22|BACBbAa相交相切相离rdrdrd2两圆的位置关系的判定方法. 设两圆圆心分别为O1、O2，半径分别为r1，r2，|O1O2| 为圆心距，则两圆位置关系如下：|O1O2|r1+r2两圆外离；|O1O2|=r1+r2两圆外切；| r1-r2|O1O2|r1+r2两圆相交；| O1O2 |=|r1-r2|两圆内切；0| O1O2| r1-r2|两圆内含 . 三、经典例题导讲例 1 直线 l 经过 P（2,3 ）, 且在 x,y 轴上的截距相等, 试求该直线方程. 错解 ：设直线

48、方程为:1byax, 又过 P(2,3),132ba, 求得 a=5 直线方程为x+y-5=0. 错因 ： 直线方程的截距式: 1byax的条件是 :a0 且 b0, 本题忽略了0ab这一情形. 正解 ：在原解的基础上, 再补充这样的过程: 当直线过 (0,0) 时, 此时斜率为 :230203k, 直线方程为y=23x 综上可得 : 所求直线方程为x+y-5=0 或 y=23x . 例 2 已知动点P到 y 轴的距离的3 倍等于它到点A(1,3) 的距离的平方, 求动点 P的轨迹方程 . 错解 ：设动点 P坐标为 (x,y).由已知 3,) 3()1(22yxx化简 3x=x2-2x+1+y

49、2-6y+9 . 当 x0 时得 x2-5x+y2-6y+10=0 . 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 3 页，共 8 页当 x0 时得 x2+ x+y2-6y+10=0 . 错因 ：上述过程清楚点到y 轴距离的意义及两点间距离公式, 并且正确应用绝对值定义将方程分类化简 , 但进一步研究化简后的两个方程, 配方后得(x-52 )2+(y-3)2 = 214和 (x+12 )2+(y-3)2 = - 34两个平方数之和不可能为负数, 故方程的情况不会出现. 正解：接前面的过程 , 方程化为(x-52 )2+(y-3)2 = 214

50、, 方程化为 (x+12 )2+(y-3)2 = - 34 , 由于两个平方数之和不可能为负数, 故所求动点P 的轨迹方程为: (x-52 )2+(y-3)2 = 214(x 0) 例 3m是什么数时，关于x,y 的方程（ 2m2+m-1）x2+（m2-m+2）y2+m+2=0的图象表示一个圆？错解： 欲使方程Ax2+Cy2+F=0表示一个圆，只要A=C 0，得 2m2+m-1=m2-m+2，即 m2+2m-3=0，解得 m1=1，m2=-3，当 m=1或 m=-3 时， x2和 y2项的系数相等，这时，原方程的图象表示一个圆错因： A=C ，是 Ax2+Cy2+F=0表示圆的必要条件，而非充