2022年高中数学平面解析几何初步经典例题.docx

精选学习资料 - - - - - - - - - etters and call initiative of leadis, and do practi cal thi ng cadre s at all levels, a ngs for the masses combi ne good, effective thr a ctive, active, focusing on building neough rea chi ng pe opl e at the servi w moment um for development, a ccelce of the "last mile". T hird, foster the devel opme erating transformation of forest devel opme nt. To imnt of new e nergy, plement the new new Ge neral Se development cretary XI Jinping stressed phil osophy. Phil osophy is ttdevelopment he acti on guiof innovati on forest restr ucturi de, new ideas and ne w devel opmng, revitalizati e nts. Carryion of the ol ng out innovad industrial bases i tion, coor dinatin Northeast China is the State's major strategy, Ce on a nd development of green, open, shared ideas, mntral has i ssue d compre hensive opini ust be measurabl e, direct action with i h ons of revitalizing Northea new development conceptst Chi na and other old i s, training cadres. In a nd ustrial bases, t he CPC Ce ntral Committee on revitalization in new dev elopment concept as a yardstick. E stablished in line Nort with the heast China wer new concer e . V igorous determi nation does not waver, the work does not sla pt of evaluation system and evaluati on criteri on, embodies tcken he new deveoff. Be firm with in the lopme nt policy, organidevelopment ha zation, mandate ims more to do with hard, a plementati on, always meand not muddl e along, passive ina ction. To rely on t heir ow sure d by the new dev elopment philosophy, continuous correctin efforts, ca n't wait, ca n't wait, stand still. T on of forest transition course. In a nehis not only provi w devel opmedes new opportunities for devel nt conce pt for the pat h command. Aopme nt in our region, and gave us s part of the impl ementation of the e new requirements. We must se ize the opportunit new devel opme nt philosophy followe d and actiy, full use of nati onal poli cy, on gui deli nes, firmly adjusted, has to be more compli corre cted and rejei cated, ct unsuita to start a nd target, give full play to t ble, ina ppr opriate a nd eve t n against he the new development ideas, behavi i ors 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 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 im m plementation "three big engineering", and create "two big environment", strengthening on new development, and new economy concept of learning, and grasp a n usi ng, real put thought and acti i on unified to new development concept up, 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 economi i c transformation and upgrading, quality and efficie ncy "first power". 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， y 1) ，B( x2， y 2) 在坐标平面上什么位置，都有d=|AB|= ( x 1 x 2 ) 2 ( y 1 y 2 ) 2，特别地，与坐标轴平行的线段的长 |AB|=| x2 x1| 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( x 1， y 1) ，B( x 2， y 2) ，P( x ， y )之间数量关系的一个公式，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x x 1 x 2A为起点， B为终点， P 为分点，则定比分点公式是 1 . 当 P 点为 AB的中点时，y y 1 y 21x 1 x 2 x =1，此时中点坐标公式是 2 . y y 1 y 223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. )说明适用条件名称方程斜截式ykxbx 0k 为直线的斜率倾斜角为 90° 的直线不b 为直线的纵截距能用此式点斜式yy 0k(x(x 0, y0) 为直线上的倾斜角为 90° 的直线不能用此式已知点， k 为直线的斜率两点式yy 1=xx 1(x 1, y 1) ，(x 2, y 2) 是直与两坐标轴平行的直线y 2y 1x 2x 1线上两个已知点不能用此式截距式x + ay =1 b0a 为直线的横截距过（ 0，0）及与两坐标轴平行的直线不能用此b 为直线的纵截距式A，C，C分别一般式AxByCBABA、B不全为零为斜率、横截距和纵截距5两条直线的夹角。 当两直线的斜率1k ,k 都存在且1k ·k -1 时，tan =k2k 1k 1，1k2当直线的斜率不存在时，可结合图形判断. 另外还应注意到： “ 到角” 公式与“ 夹角” 公式的名师归纳总结 iveli with fhood, i s related to people's welleasible poverty standarll-being ads, state car d, bnd social uilt on the basiharmony a s ofnd sta documebility. We need to nt management. To firmprotect a ly establish thend impr "poverty redove the livel uihood of the pe ction" conceopl cee as the starti pt, increase the ing point and ending ntensity of resourcg poi nt of transition and improve forest e i ntegration, a nd relate d funding, witpeople's feeli h limited funds wing and wihappiness. sely. By using a To promote poverty relief and a combination of employme devel me nt, entre opment w re prene uork. Impl rship for l ementing poverty allevpoverty eradi cation poverty eraiation cr eraucial proje dicati on, ect is a major strategi c ducation, poverty allevide cision made ation, medical aiby the CPC Central Committee, is also aid of poverty means, due tdeterm o effects of poliine d by the cies, those policieprovi ncial "first project", we must s, ensure the com pletion of missi unify think i on obje ing and acti ctives for poveon to t rty eradicahe requirements ti on for tof the Ce he year. To activelntral, provi y ncial prol , resolmote the coutely win t nstruction t he poverty battle. The previ of new t owns. In Fe ous e bruary thipha se I to 18 stations, Tahe, s year, promulgated by tPine Ridg he State Counce research, visite il on further promotid many of the poor, go, the moting urbanizati on cheavier, more pressure. For poverty relief aonstruction of new opi nions, proposed nd development work, to adhere to the pe ople-cenwe must pay attenti tered, four modernization to it, alway ons synchronizati s in mind, graspi ti on, optimization, e ng ha nds, shoul n, e col ogy civilizati d not be bl ati on aindly optimisti nd cultural ti c, therheritage of ne e can e w be no sla w urbanizatia ck. Poverty alleviation and devel on pat h with Chi nese l opment lichara cteristics. Accordinges in pre to cise, a distccurate. Pre rict -wide conssent, i truction of cn order t ivilio find out the zed city and t real bast he beae of poo utiful cor people as untrysides soon as , further strepossi ble, come up ngthe ning of urban 第 1 页，共 8 页transport, water supply a with the stea dy work ofnd drai i nage and sew age, waste di i sposal ground, underground, such as i i nfrastructure construction, strive to create a safer and mor r e livable environment. To actively seize the full stop and opportunities for poverty alleviation and development, further efforts to increa se forest villages merge, population to the County (district) Council sites and centres s concentrated in vill l ages and towns. Combined development of urban construction and tourism industries, careful pla la nni ng and constr tr ucti on of a number r of suitabl l e for residential and farm tour towns and villages, forming one vill age 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 ehearte e d support to and pr r aise, this work will carry on, absolutely ca nnnot or movement. Grassroots masses and cadres in combination with poverty reduction, combined - - - - - - -精选学习资料 - - - - - - - - - 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l 1yk 1xb 1， l 2y2k 2xb 2，有以下结论： l1 l2k =k ，且120，l 2A 2xB2yC0，当 A 1， A 2， B 1， l 1 l 2k ·k = -1 （2）对于直线 l 1A 1xB 1yC 1B2都不为零时，有以下结论： l 1 l 2A = A 2B 1C 1l ：AxlByC0，则点 P 到直线 l 的距离B2C2 l1 l2A1 A2+ B1 B2 = 0 l 1 与 l 2相交A A 2B 1B 2 l 1 与 l 2重合A = A 2B = B 2C 1C27点到直线的距离公式. （1）已知一点P（x 0, y0）及一条直线d=|Ax 0A2By02C|；0，2:AxByC20之 间 的 距 离B（ 2 ） 两 平 行 直 线 l1:AxByC 1d=|C 12C2|. AB28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：(xa )2(yb)2r2，其中（ a ，b）是圆心坐标， r 是圆的半径；名师归纳总结 （2）圆的一般方程：x2y2DxEy. F0（D2E24 F 0），圆心坐标第 2 页，共 8 页为（ -D ，-2E ），半径为 r = 2D2E24 F2- - - - - - -精选学习资料 - - - - - - - - - etters and call initiative of leadis, and do practi cal thi ng cadre s at all levels, a ngs for the masses combi ne good, effective thr a ctive, active, focusing on building neough rea chi ng pe opl e at the servi w moment um for development, a ccelce of the "last mile". T hird, foster the devel opme erating transformation of forest devel opme nt. To imnt of new e nergy, plement the new new Ge neral Se development cretary XI Jinping stressed phil osophy. Phil osophy is ttdevelopment he acti on guiof innovati on forest restr ucturi de, new ideas and ne w devel opmng, revitalizati e nts. Carryion of the ol ng out innovad industrial bases i tion, coor dinatin Northeast China is the State's major strategy, Ce on a nd development of green, open, shared ideas, mntral has i ssue d compre hensive opini ust be measurabl e, direct action with i h ons of revitalizing Northea new development conceptst Chi na and other old i s, training cadres. In a ndustrial bases, t he CPC Ce ntral Committee on revitalization in new dev elopment concept as a yardstick. E stablished in line Nort with the heast China wer new concer e . V igorous determi nation does not waver, the work d pt of evaluation system and evaluati on criteri on, embodies toes not sla cken he new deveoff. Be firm with in the lopme nt policy, organidevelopment ha zation, mandate ims more to do with hard, a plementati on, always meaand not muddl e along, passive ina ction. To rely on t heir ow sure d by the new dev elopment philosophy, continuous correctin efforts, ca n't wait, ca n't wait, stand still. T on of forest transition course. In a nehis not only provi w devel opmedes new opportunities for devel nt conce pt for the pat h command. Aopme nt in our region, and gave us s part of the impl ementation of the e new requirements. We must se new devel opme nt philosophyize the opportunit y followe d and actiy, full use of nati onal poli cy, on gui deli nes, firmly adjusted, has to be more compli corre cted and rejei cated, to start a nd target, give full play to t ct unsuita ble, ina ppr opriate a nd eve t n against he the new development ideas, behavi i ors 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 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 im m plementation "three big engineering", and create "two big environment", strengthening on new development t , and new economy concept of learning, and grasp a n 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 must rely on Science and technology affects. echni cal innovation is the promotion of economi i c transformation and upgrading, quality and efficie ncy "first power". 二、疑难知识导析1直线与圆的位置关系的判定方法. 0；圆：x 2y2Dx)EyrF0. （1）方法一直线：AxByCAxByC0消元一元二次方程2判别式0相交0相切x2y2DxEyF0b24 ac0相离22，圆心（ a ，b）到（2）方法二直线 :AxByC0；圆：(xa )(yb直线的距离为d r 相离d= | Aa2 Bb2 C |d r 相切A B d r 相交2两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|> r 1+r 2 两圆外离；|O1O2|= r1+r2 两圆外切；| r 1- r 2|<|O 1O2|< r 1+ r 2 两圆相交；| O 1O2 |=| r1- r2| 两圆内切；0<| O 1O2|<| 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 ：设直线方程为 : x y 1 , 又过 P(2,3),2 3 1 , 求得 a=5 a b a b直线方程为 x+y-5=0. 错因 ：直线方程的截距式 : x y 1 的条件是 : a 0 且 b 0, 本题忽略了 a b 0 这一情a b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 : k 3 0 3, 2 0 2直线方程为 y= 3 x 2综上可得 : 所求直线方程为 x+y-5=0 或 y= 3 x . 2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 . 名师归纳总结 错解 ：设动点 P 坐标为 (x,y).由已知 3x mis(x1 )2(y)32,on to it, alway ons synchronizati y s in mind, graspiti on, optimization, eng ha nds, shoul col ogy civilizati d not be bl ati on andindly optimisti cultural heritagc, ther e of nee can w urbe no sla banizatick. Poverty alleviation and develon path with Chi nese characopment li cteristics. According to es in pre to cise, a districtccurate. Pre t-wide constrsent, in order t uction of civili t o find out the real zed city and tl base he bea utiful of poor countrysidepeople as , furtsoon as er strepossi ble, come up ngthe ning of ur ban 第 3 页，共 8 页化简 3 x =x2-2x+1+y2-6y+9 . ous pha i s yese I to 18 stations, Tahe, s year, promulgated by thePine Ridg State Council e research, visite on further promoti d many of the poor, go, the ti ng ur banization construction heavier, more pressure. For poverty relief aon of new opi nions, proposed to adhere to the pe