二阶曲线极点-极线理论在初等数学中的应用-张家兴

,,.3.,,,,,,,,.,.(1),,,.(2),,.(3),,.,..1::C22AxBxyCyDx+++0EyF++=00(,)Pxy(PC),PC12,MM,1PMQ(12MM,PQ)=−1(),Q:L:(0x0y1),222ABDBCEDEF⎛⎞⎟⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎟⎜⎝⎠1xy⎛⎞⎟⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎜⎟⎟⎜⎜⎝⎠=0.LP;PL.(12MM,PQ)1M2MPQ1M2MPQ,(12MM,PQ)=1221MPMQMPMQ⋅(1MP,2MP,2MQ,1MQ).,(12MM,PQ)=−1,Q12MM,P.,C:2AxBxy++20CyDxEyF+++=,00(,)PxyL:0000(2)(2)AxByDxBxCyEy++++++0020DxEyF++=.,00(,)Pxy,C:20xxx⇒;20yyy⇒;00()/2xyxyyx⇒+;02xxx+⇒;02yyy+⇒.,:1PC,LCP[1].2PC,L(:PC).3PC,LP[2].:1C:22AxBxyCyDx++++0EyF+=,00(,)PxyP,000022AxByDkBxCyE++=−++.00(,)PxyL:0000(2)(2)AxByDxBxCyEy++++++200710310020DxEyF++=.PTCMN.(,)1MNPQ=−PMN,Q.TQL.//TL:000022AxByDkBxCyE++=−++2,[3].2:1(86)C:22143xy+=,m,L:y=4x+m,C.:PQCL,M00(,)xy:MPQPQL1,MPQ0034xky=−PQL003414xy−×=−:00yx=ML,004yxm=+000034144xyyxm⎧⎪⎪−×=−⎪⎪⎨⎪⎪⎪=+⎪⎩:003xmym⎧=−⎪⎪⎨⎪=−⎪⎩M,PQ,()2231043mm+−13m24221313m−2:(94):221369xy+=(4,2),()(A)20xy−=(B)240xy++=(C)23120xy+−=(D)280xy+−=,00(,)xy001369xxyy+=(4,2)421369xy+=1922yx=−+:12(4)2yx−=−−:280xy+−=(D)3,OPOPAPBPMN(AB,MN),AB,PMNQ.2,ABOP,:1MPNQNPMQ⋅=−,,:MPNQNPMQ⋅1=,:MPNQNPMQ⋅=⋅.:3,OPOPAPB(AB),AB,POMN,ABQ,:MPNQNPMQ⋅=⋅(,)4:.4LP,PL().:PBAPCD;ADBCE;BDACF;EFLMN;MN.,PEF,EFP,MN.[1]:,199413,23.123.123.2[2]:,200042PNMBAQEMDLACFPBN32200710