xxyy,xy(x,y，B(x,y)：x1212221122(x,y，B(x,y)yb(kA1122kx，ykxb則y1122(xx)(yy)(xx)()kxx)2222221212121212kxx)4xx]221212111(xx)(yy)(xx)(yy))(yy)AB222221212k1k212k2121)[(yy)4yy]2。k12122:ykxb,l:ykxbkk1l11122212v0v12bcbxc0(a0)x,x,xx12axxx1。2122aaxy22l:y1C:1m4mxy22:y10，C:1mm4l4mxy22:y1C:1m，且4m1且4mm。l4m1l:ykx1過定點(diǎn)（）l:yk(x1)過定點(diǎn)（，0）l:y2k(x1)過定點(diǎn)（，2）N：yl2xxABEBx0x0。:yk(xk0(x,y)B(x,y)。l，，，1122yk(x1)由消yk2x2(2kxk022①2yx(2k1)4k4k10224210k即2②42k12k1122xx,xx1(,)。2k2k12k21221112k11E(2k2112k22y(x)令得x2kk2k2022113E(ABd為。2k22214k1k22(xx)(yy)d1k2222k1212k2314k1k2k395221kx2k。2k13320x2y32ab：x軸2ab22A。12:xttl與x點(diǎn)PTlN122c3x2e，a2cb1y1C224ayk(x2)(x,y)N(x,y)AM1kAM1yk(x2)（M，,1消y4y4112211x2216k428kx212121(k)1616和x2x整理得21221是方程的兩個根，則，14k14k2112114k28k4k21y1M(,)，1114kkk14142122118k24k22(,)2ANkN221414kk2222kk2yyyyyktykt，，112212kk1txxxxp1p2121xyxy4令x2112xNyyt1244433t202(3t又，tt43t3x2y22(ab0)AC：1a2b02ACBCECE，3x2OACBC0A點(diǎn)C2(為。x2y22a23Ab1(4，ECb2x2y21124x3kk3y3k(xy3(1k)3(1消k)ykxx3y12022k)x6kk)x9kk303x2229k18k39k18k39k18k3222xx3即x1k3(1k)3(1k)P2Q2P212k3(13)yykx3(1k)kx3(1k)k(xx)2k＝＝PQPQPQk9k18k39k18k336k22yyx13x＝xkPQPPQ3(1k)3(1k)23(1k)PQ22xQ1。3x2y21：于PQll=94ì=?xlxl?Q\即12=lí11221122?=3+(-3)lyy?12ykx3k0y消y4x9y3622(49k)x54kx450QM22(54k)445(49k)144k09k522＝2即2①54k(xx)xx2xx,xx1221249k49k122122xx1xx22154k)29k442221即②45(49k))29k9k2221135(1)91501，59k5522105或x。51,5l。5x22y261,3。：3ab24C3lCBOl2x26c1。b1，，y2c3a3a，(xy)B(x，y)⊥x3A，AB與xAB11223ym3m22k2。ABm(41k2mkx6kmxm30，把y22263(m1)1)2AB(1kxx)()k2mm2xx22，。22xx1)k2k1122k23121k2312k2212(k1)(3k1m)k1)(9k1)2222212k12122。33(k0)≤34k1)k21222961236k4k29k62k2139kk0AB3，2k3k22max。133當(dāng)△SAB。222max2BNCOyl被以為直徑的圓截得弦長恒為定值？若存在，求出l的方程；若不存在，說明理由。NNAxx與11225221xSS2pxxy得xxxS222.21212y12xp(xx)4xxp4pk8p2pk2.＝px2＝22222121212kS22p.2,與為直lOtACxyp,,12121OP）()y2p1為OHOx21yp2＝2.112221yp111OHa2,()(2)aypPH2OP2OH2=y21p2ayp21224411p(a)ya(pa＝21pPQ2(2PH)4()().2=ayapa22ppa0a,p令l存22py，2.：1kxx1k(xx)4xx1k4pk8p22222221212122p1kk2.＝222p1kd.2112pdAB2p1kk22pk2,S222222ABN1k2kS22p.2t(x0)(xx)(yp)(yy)116xxx(ap)(ay)211p＝x4(ap)(ay)4(a)1a(pa).2121lPxx2244ppPQxx4(a)ya(pa)2(a)ya(pa).223411ppp0,得a,此時PQpy令al.222P6.P的2＝·P.1PN.xy22ac51.=22952,得由①1P4,NPMNMN2PM2PN22PMPNcosMPN.②4PMPN2(PMPN2).222x2PN23y1.23x2y21P955945,x332y2x,2x3y3.225.y2335,332-5-335，）或（332-5.即P(222222xy22:ab(F(CMab212CP,BABClQ足，7Q解2c221x2y214,2142ab22a2b2cab222(x,y),(x,y),(x,y)B。1122APAQ,,,PBQB01且則,又Qxxyy4x1y，，121211xxyy1212112xxyy2222224x，y，））1121212BCx2yx2y2121222224s2y4Q(x,y)2xy20上,,,(x,y),(x,y),B(x,y)Q1122PAPB且AQQB又P,,Q,B,(4x1yx,y））14x1111yx2,y112(x,y),B(x,y)x2y4,ACC221122(x2y4)4(2xy2)140222）(x2y4)4(2xy2)14022288(xy20得∵∴2xy20Q(x,y)2xy20上x2設(shè)F、F12y124·P12(0,2)MlA、BOl的k,Pxybc3,aFF12x123x,y,3x,yxy3x133x8222244122,2x0P2x122P1當(dāng)x12,Pxybc3,aFF12222FF1F21212121212212122x3yx3yxy322222l:ykxAx,y,Bx,y，0x1222ykx214x4kx30yk22x2y1244k3x,xx∴x14141212kk2291334k4k34k30kk或2由242200B90cos0B0OAOB0OAxxyy0又00∴1212k8kk122222kxxkxx44又yy12121212121414kk2k2243k1204∴k22∵k2141kk224332k或k222x2y2126）O，ab22EOBE且OAx2y21261，）,ab22421a2118a2b211a2x2y2848E4b2611a2b24b2OBE且OAykxmmx2(kxm)82k)x4kmx2m80即y得22222,x2y218416km2k)(2m8)km4)0km40=222222即224kmxxk2(2m24k2m2m2k22,yy(m)(m)kxxkm(xx)mm要又12k2221212k12k12k121212122222m82xx1212k2OAOB,xxyy0,即2m8m8km822220m8k80k20使,22,12k12k812122210,283263263m2km40mmym,m2,即或,22m8282