仿射变换观点下的中学椭圆问题

ANLIPOUXI732013.17◎赵桂梅(长春市十一高中130062)【】．【】．．．、．、、．、．1．2．3m00()1kkmaba'b'a·b=m2·a'·b'．1201120Oe=槡22x=2槡2．12P→OP=→OM+2→ONMN．OMON－12F1F2PF1+2PF2F1F2．．x24+y22=1．OMON－1．→OP=→OM+2→ON→OP．2槡22001Cx2+y2=2．kOM·kON=－12kO'M'·kO'N'=－1．O'M'⊥O'N'→O'M'=→O'N'=槡2．→O'P'=槡5P'x2+y2=10．∴Px220+y210=1F1F2F1－槡10()0F2槡100．．22009x2a2+y2b2=1a＞b()＞0A－a0lQR．lmP．|AQ|槡2|OP||AR|．．ba001x2+y2=b2．x'B'O'Q'B'R'．△O'A'Q'△R'A'B'∠A△O'A'Q'∶△R'A'B'A'Q'A'B'=O'Q'A'R'．A'B'=2O'P'O'Q'=O'P'2O'P'2=A'Q'·A'R'2|OP|2=|AQ|·|AR|．∴|AQ|槡2|OP||AR|．．【】1S．L．．．1986．2．．1987．3．．1983．