关评讲《劝学》-单元过轴的交点为定值。与证明中点的轨迹方程;求弦的顶点作互相垂直的二过抛物线xABABOBOAxyP)2()1(,,2:92135.FxOyBAM,:kxylOA解:设xkylOB1:则xykxy22联立22,2kxkyAAxyxky212联立22,2kxkyBB2200BABAyyyxxxkkkk11222)1(2 kk22xy轨迹方程::11:140Pxy.O.1PM2P P),(),,(),,(00222111yxPyxPyxP解:设相减:由121222222121yxyx2121212121yyxxxxyy00121yxk002xyk 又2121kk.FxOyP:12:140P的中垂线上在若为正三角形,则OFP)22,4(ppP则pOP43||4||pOF 而||||OFOP 9090PF或则若为等腰直角三角形,90)2(=若 P1OPk则22OPk而90)1(F若pPF ||则2||pOF 而|)||(|PFOF :16:140PxOy)4,1( BA解3202xxyayx-032axx0)3(41a)413,(a另解:)( )32,(2RxxxxP任意一点为抛物线设232axxd0dRx,都有对任意的Raxx解集是即0324130)3(41aa=没有交点?与线段AB:22:141P.FxOyPMN),4(2bbP解:假设存在这样的点),(),,(2211yxNyxM设0),4(),4(222121bybxbybx则0))(()4)(4(212221bybybxbx即4,4222211yxyx0))(()44)(44(21222221bybybyby0]116))(()[)((2121bybybyby0116))((21byby0116))((21byby:22:141P.FxOyPMN),4(2bbP解:假设存在这样的点xyxky4)5(22020842kykykyykyy820,42121016)(22121byybyy01648202bkbk时,方程恒成立当2b)2,1(P存在这样的点:22:141P.FxOyPMN286:xylMN解:假设)314,56(),4,4(NM则),4(2bbP设0)314)(4()456)(44(22bbbb即)2,1(P)1(12:),1(2:xkylxkylPNPM则设24,1444)1(222kykkxxyxkyMM24,1442kyNkkxMN同理)144(124:22kkxkkkkylMN定点过)2,5( 作业:试卷