上海市复旦附中2017-2018学年高二上学期期末考试数学试题

上海市复旦附中2020-2021学年高二上学期期末考试数学试题10yA1,2y5x2A2xy2214,29cosxR（y2sin2xyxy22221a01aa24934x2y1F和F22P12FFPF12121PAPF取4xy2F和APPx2y2x2y1201x2y21|PF|=6FF、，，P4b2121PFPF0124,022PM:xy8xQM，QP04x,B52yrryxl222点MM.4rlAB:mxym10l:xmym10l与PAB12C:x1y14AB23|PB|22．022）bxxyyDyrr0Pa,bab0．已知Ox2O22Pmnaxbyr2）．mnOn．mnnOmnnn．与OD．mnOxy22P,P,P,,P1nPFFn123n1n）2pxp0FA、y2BlAMFMFO）:y4x,ABLC2y2x4LAB）OLAOB22Lx2y2:1．C43C）CAPAP:xy4CNCO22（）MPOPOMONPAC与xA3点，B点NCONmOAnOBmn3x2y2:1ab0P1,1P0,1P、C、、1223a2b23P中恰有三点在椭圆C24Cy1CM、NxMNPCA、两点，若直线PAPBlB222l:2a2xby2b40a,bRab44abx0x2ya2b．x24yp.由题得抛物线的准线方程为y1p2224y.xpx224yx2.2y5．xAy2k(x1),利用直线和圆相切得到kA.A1,22k(x1),即因为125y22k2(1)125k，k2211xy20，22x2y5，2y5xAxByCP(x,y)l:C0点d00.00AB221．2A(x,y)B(x,y).(4,2)，是1122x2y2x2y2xx8,yy41，11122991212x2x21y2y201，229yyxx12yy1k212121．xx4(yy)xx2212121y3．x2cosx22.x2y21,x2y3.y2sin2cosx22y2sin2y3x2.:x2y3参：通过方程计算出sincos，再利用三角恒等式sinacosa1.224a493a.2a49324cab.c2a2b22223．2123PF|PF|2PFPF22PFPF11212121PFPF12.111133,bcc.a22242424213PF|PF|2PFPF22211212PFPF12PFPF1121133PFPFsin2S.232221232.1(．4PPAAP作A作，141.PAP为141.．454cos{，23sin443455455＝＝33＝3，53当4551d＝min362arctan．2PF22PF2，PFPF0,PFPF，212121bb6,S2022126yx，2622arctan62arctan2xy2214﹣23，x2y21M4x2y214MMPPMP(x,y)M)xf)yg(）xtymyBxy，Axl，11224xyty4m02ly2yyt，yy4m则16t16m0，21212xxtymtymtm则21212t2tMABABMCC00t01当tKK11即m32t2t2m5t把m32t16t16m0223t00t322ABC5m1t222t1td21tr即222r4x0x5r，当t2l0r54l4rxtymyBxylAxl，，1122y24xAB的坐标，分别讨论t0Mt0时r．422P|PB|）+（）x2y2⊥|PA|=2PDxy11为2DD2P|PB|∵：﹣3与：+3，lymlxm12∴⊥，llll1212）+（），Px2y2⊥，=2（），22xy11,2D2则|PA|=|PCCAPCCB2PCCD2PD|，21213212D22，P|3212221，|PB|4224Dbxyy22abbxyy22aaD.AmPnnPb和rnmP，am，ban，bmr2na2b2Pabr，222|r2∴|n.a2b2Ard②dr直线与圆相交；dr直线与圆相切；r直线与圆相离.③dCF1nab．22PnP．1n2，n121由，n1n．CnP．nB取，FB以l，x，，，Bx）35）xy1.AB））my1xA、BAOB42yyyy22和.mA1212））AB35、B1my112yy142，xyy2122(yy)(yy)4yy，221212124my40y2，y4myy4，∴y，1212∴16216321，mmy1，∴xxy1.lyy42.12y2x237x2y21）或）13x2y2和设P（x,）1，4mm72x4yx8x222PA4x2y21m0m100m25，m0，4mmy2x2x2y2mm1或33747321（x,4x8x2x2y227.3xx,yN(x,y)设Px，1OPOMONy4111Bmnmn1P22mnxx3P,yN(x,y),x3,y4设，ONOPOM1y4，111x3y44.3y44∴x22P22）2mn,nONmOAnOBy，,x222mnn4mn122222m2n22mnmnmn2222222n22mn4mn21mn∴m22.MMPPPM(x,y)M)xf)yg(2,1x2y2））141P、P、P23441,yxmMN为MNDD335:ykxbb2kl:ykx2k1设I33()21P、P、P221,234a21x2y21.41ba22yxmMNDkkMN为，12114153kkl:yxxy1,yx:D，l443314:ykxb210，Ik2kbxb2b1xxy11y12kbkk2k2k1b2k1122xx2xx12b1PAPB221l:ykx2k12,1.R(x,y)f(x,y)f(x,y)0fxyi(,)(1,2,3)if2123(x,y)0f1x,y(,)0fxy2f(x,y)032y1或y0）xx1100ymyy2xmym24xbyb4001b0，xb2,1,1111，qby2p和，p2a，ab4bx22a2xb40b0，x1622a20,当bbab22y2x1ymy1002xmy，m22y1y0或x4444xbyb400，x1b0，y210bbx。，2bb,1,1111，qby2p和，p2a，4bx22a2xb40b0a2b2160，xa2a2ab0224当b，a2b2，2022b0f10，0a224f②2b2，a4b40，ab162200aa20b0，224③a2b2，，，，ff，，bf10a，4b4，20a2b22000b0，224④a2b2bf10a，4b4，ab22第3,bab22R(x,y)f(x,y)f(x,y)0fxyi(,)(1,2,3)if2123(x,y)0f1x,y(,)0fxy2f(x,y)032y1或y0）xx1100ymyy2xmym24xbyb4001b0，xb2,1,1111，qby2p和，p2a，ab4bx22a2xb40b0，x1622a20,当bbab22y2x1ymy1002xmy，m22y1y0或x4444xbyb400，x1b0，y210bbx。，2bb,1,1111，qby2p和，p2a，4bx22a2xb40b0a2b21