5G移动网络发展蓝图.pdf
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1、k 1 PQ QA , 11 1 44 (,4 )(,) x y kk . 1 1 1 4 4 4 4 k kx x k .同理 1 2 4 4 kx . 12 12 448 443 kx kx . 即 2 12 1 2 25 () 8 0 kxx kx x . (*) 又 2 2 4 1 3 yk x y x 消 去y得 22 (3 ) 8 19 0 kx k x . 当 2 30 k 时,则直线 l 与双曲线得渐近线平行,不合题意, 2 30 k .师出教育 电话 :400-600-2690 咨询 QQ:1400700402 第 5 页共9 页 C B A o y x 由韦达定理有: 12
2、 2 12 2 8 3 19 3 k xx k xx k 代入(*)式得 2 4, 2 kk . 所求 Q 点的坐标为 (2 ,0 ) . 考点 7 利用向量处理圆锥曲线中的最值问题 利用向量的数量积构造出等式或函数关系,再利用函数求最值的方法求最 值,要比只利用解析几何知识建立等量关系容易. 例 7设椭圆 E 的中心在坐标原点 O,焦点在 x 轴上,离心率为 3 3 ,过点C( 1,0) 的直线交椭圆 E 于 A、B 两点,且CA 2BC ,求当 AOB 的面积达到最大值时直 线和椭圆 E 的方程. 解答过程:因为椭圆的离心率为 3 3 ,故可设椭圆方程为 22 2x 3y t(t 0) ,
3、直线 方程为 my x 1 , 由 22 2x 3y t my x 1 得: 22 (2m 3)y 4my 2 t 0 ,设 11 22 A(x ,y ),B(x ,y ) , 则 12 2 4m yy 2m 3 又CA 2BC ,故 11 22 (x 1,y ) 2( 1 x , y ) ,即 12 y2 y 由得: 1 2 8m y 2m 3 , 2 2 4m y 2m 3 , 则 AOB 1 2 2 1m S| y y | 6 | 22 m 3 66 3 2 2|m| |m| , 当 2 3 m 2 ,即 6 m 2 时, AOB 面积取最大值, 此时 2 1222 2 2t 3 2 m
4、 yy 2m 3 (2m 3) ,即t1 0 , 所以,直线方程为 6 xy 1 0 2 ,椭圆方程为 22 2x 3y 10 . 小结:利用向量的数量积构造等量关系要比利用圆锥曲线的性质构造等量关系 容易.师出教育 电话 :400-600-2690 咨询 QQ:1400700402 第 6 页共9 页 考点 8 利用向量处理圆锥曲线中的取值范围问题 解析几何中求变量的范围,一般情况下最终都转化成方程是否有解或转化成 求函数的值域问题. 例 8 已知椭圆 2 2 1 2 x y 的左焦点为 F,O 为坐标原点. (I)求过点 O、F,并且与椭圆的左准线l 相切的圆的方程; (II)设过点 F
5、且不与坐标轴垂直的直线交椭圆于 A、B 两点, 线段 AB 的垂直平分线与x 轴交于点 G,求点 G 横坐标的取值范围. 考查意图: 本小题主要考查直线、圆、椭圆和不等式等基本知识,考 查平面解析几何的基本方法,考查运算能力和综合解题能力. 解答过程:(I) 22 2, 1, 1, ( 1,0), : 2. abcFl x 圆过点 O、F, 圆心 M 在直线 1 2 x 上. 设 1 (, ) , 2 M t 则圆半径 13 ()(2 ). 22 r 由 , OM r 得 22 13 () , 22 t 解得 2. t 所求圆的方程为 22 19 ()(2 ). 24 xy (II)设直线 A
6、B 的方程为 (1 ) (0 ) , ykx k 代入 2 2 1, 2 x y 整理得 22 2 2 (1 2 ) 4 2 2 0. kx kxk 直线 AB 过椭圆的左焦点 F, 方程有两个不等实根. 记 11 22 ( , ), ( , ), AxyBxyA B 中点 00 (,) , Nxy 则 2 12 2 4 , 21 k xx k AB 的垂直平分线 NG 的方程为 00 1 () . yy xx k 令 0, y 得 222 00222 2 21 1 . 212121242 1 0, 0, 2 G G kkk xxk y kkk k kx 点 G 横坐标的取值范围为 1 (,
7、0 ) . 2 考点 9 利用向量处理圆锥曲线中的存在性问题 y l G A B F O师出教育 电话 :400-600-2690 咨询 QQ:1400700402 第 7 页共9 页 P Q C B A x y O 存在性问题,其一般解法是先假设命题存在,用待定系数法设出所求的曲线 方程或点的坐标,再根据合理的推理,若能推出题设中的系数,则存在性成 立,否则,不成立. 例 9已知 A,B,C 是长轴长为 4 的椭圆上的三点,点 A 是长轴的一个顶点,BC 过椭圆的中心 O,且AC BC 0 ,|BC| 2|AC| , (1)求椭圆的方程; (2)如果椭圆上的两点 P,Q 使 PCQ 的平分线
8、垂直于 OA,是否总存在实数 , 使得PQ AB ?请说明理由; 解答过程:(1)以 O 为原点,OA 所在直线为 x 轴建立 平面直角坐标系,则A(2,0) , 设椭圆方程为 22 2 xy 1 4b , 不 妨 设C在x轴 上方, 由椭圆的对称性, |BC| 2|AC| 2|OC| |AC| |OC| , 又AC BC 0 AC OC ,即 OCA 为等腰直角三角形, 由A(2,0) 得:C(1,1) ,代入椭圆方程得: 2 4 b 3 , 即,椭圆方程为 22 x3 y 1 44 ; (2)假设总存在实数 ,使得PQ AB ,即AB/PQ , 由C(1,1) 得B( 1, 1) ,则 A
9、B 0(1 )1 k 2(1 )3 , 若设 CP:yk ( x1 )1 ,则 CQ:yk ( x1 )1 , 由 22 22 2 x3 y 1 (1 3k )x 6k(k 1)x 3k 6k 1 0 44 yk ( x1 )1 , 由C(1,1) 得x1 是方程 22 2 (1 3k )x 6k(k 1)x 3k 6k 1 0 的一个根, 由韦达定理得: 2 PP 2 3k 6k 1 xx1 13 k ,以 k 代k得 2 Q 2 3k 6k 1 x 13 k , 故 PQ PQ PQ PQ PQ yyk ( xx)2 k 1 k xx xx 3 ,故AB/PQ , 即总存在实数 ,使得PQ
10、 AB . 评注:此题考察了坐标系的建立、待定系数法、椭圆的对称性、向量的垂直、 向量的共线及探索性问题的处理方法等,是一道很好的综合题.师出教育 电话 :400-600-2690 咨询 QQ:1400700402 第 8 页共9 页 考点 10 利用向量处理直线与圆锥曲线的关系问题 直线和圆锥曲线的关系问题,一般情况下,是把直线的方程和曲线的方程组 成方程组,进一步来判断方程组的解的情况,但要注意判别式的使用和题设中 变量的范围. 例 10设 G、M 分别是 ABC 的重心和外心,A(0, a) ,B(0,a)(a 0) ,且 GM AB , (1)求点 C 的轨迹方程; (2)是否存在直线
11、 m,使 m 过点(a,0) 并且与点 C 的轨迹交于 P、Q 两点,且 OP OQ 0 ?若存在,求出直线 m 的方程;若不存在,请说明理由. 解答过程:(1)设C(x,y) ,则 xy G( , ) 33 , 因为GM AB ,所以GM/AB ,则 x M( ,0) 3 , 由M为 ABC 的外心,则|MA|MC| ,即 22 22 xx ()a ( x )y 33 , 整理得: 22 22 xy 1(x 0) 3a a ; (2)假设直线 m 存在,设方程为yk ( xa ) , 由 22 22 yk ( xa ) xy 1(x 0) 3a a ONFederal prosecu- to
12、rs charged dozens of wealthy parentsincluding prominent law and business figures and two Hollywood actresseswith using bribes, bogus entrance- exam scores and faked athletic achievements to get their chil- dren admitted to elite colleges. One New York law-firm co- chairman allegedly paid $75,000 to
13、an admissions con- sultant so his daughter could a portion of the funds funneled to the then-head tennis coach at Georgetown University, in exchange for having their daughter tagged as a recruited athlete. She was admitted to the school. Joseph Bonavolonta, special agent in charge of the Federal Bur
14、eau of Investigation Boston field office, described on Tues- day a “culture of corruption and greed that created an un- even playing field for students trying to get into these schools the right way, through hard work, good grades and commu- nity service.” The sprawling case, the re- sult of a 10-mo
15、nth multiagency PleaseturntopageA4 fly to Los Angeles and take the ACT in a private room last De- cember, accompanied by a proctor who had been paid to correct her errors. Another family allegedly made a $400,000 contribution to a sham charity in 2016, with ByMelissaKorn, JenniferLevitzand ErinAilwo
16、rth WealthyParentsAreCharged InCollege-EntranceScheme ChineseHackersAttack Navy,ReviewConcludes WASHINGTONThe Navy and its industry partners are “under cyber siege” by Chi- nese hackers and others who have stolen national security secrets in recent years, ex- ploiting critical weaknesses that threat
17、en the U.S.s stand- ing as the worlds top military power, an internal Navy re- view concluded. The assessment, delivered to Navy Secretary Richard Spencer last week and re- viewed by The Wall Street Journal, depicts a branch of BYGORDONLUBOLD ANDDUSTINVOLZ U.S.FightsHuaweion UnderseaDataGrid America
18、triestoblockChinesetechgiant fromexpandingsystemofinternetcables first crash in October, Boeing is making a significant change to the software that controls a stall-prevention feature, and that change is more extensive than what many industry offi- cials familiar with the discus- sions had anticipat
19、ed. Tuesday started with Aus- tralia, Malaysia and Singapore deciding to suspend the planes operations, joining China, Indonesia and several carriers in Latin America. Then, European aviation regu- lators broke ranks with their U.S. counterparts and grounded the aircraft, forcing some planes to retu
20、rn to their departing airport midflight. The suspensions marked an unusual departure for foreign regulators, who typically ad- here to guidance from the U.S. Federal Aviation Administra- tion regarding U.S.-built air- craft. President Trump wrote Tuesday on Twitter that “air- planes are becoming far
21、 too PleaseturntopageA12 Boeing Co.s woes escalated as European aviation regula- tors joined Asian and Latin American authorities in grounding the 737 MAX jet, and lawmakers on Capitol Hill urged U.S. airlines to volun- tarily park those planes after two deadly crashes of the air- craft in the past
22、five months. The crashes have raised questions about the planes flight-control system. The Wall Street Journal reported Tues- day that in response to the BYROBERTWALL ANDMATINASTEVIS-GRIDNEFF EuropeGroundsBoeingJets, BreakingFromFAAStanceLatest Brexit vote unsettles companies. A6Defeat gives rise to
23、 a range of possible outcomes. A6 The Middle Seat: Muted response over air rules. A12 Boeing is making change in cockpit software. A13The man behind the cheating scandal. A4 Prosecutors charge 33 parents in alleged scheme. A5 Clockwise from upper left: Actresses Felicity Huffman and Lori Loughlin; c
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