tuyển tập các bài toán hình học 12 ôn thi

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tuyển tập các bài toán hình học 12 ôn thi

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Bi 1.   ( ) : 2x 3y 3 0D - + =   ( ) M 5;13-  ! "# $ ( ) D  %&' d : 3x 2y 11 0+ - =  Bi 2.  !!" ()*+ $ ( ) ( ) ( )  A 1; 1 , B 2;1 , C 3;5- -  1, "#)-./0)*12()*+ 2,3453()*1 %&'1, AH : 4x y 3 0+ - = 2, ( )  ABK S 11 vdt D =  Bi 3. #$%&'()!!* ' ( ) 1 : 4x 3y 12 0D - - =  ! ( ) 2 : 4x 3y 12 0D + - =  1,678927#:; ( ) ( ) 1 2 ,D D  !< Oy  2,= !:7.3>7#? %&'1, ( ) ( ) ( ) 1 2 1 2 A 0; 4 Oy B 0;4 Oy C 3;0 ì ï - = D Ç ï ï ï ï = D Ç í ï ï ï = D Ç D ï ï î 2, ( )  4 Tâm I ;0 3 4 Bk : R d I;AB 3 ì æ ö ï ÷ ï ç ÷ ï ç ÷ ç ï ÷ ç ï è ø í ï ï ï = = ï ï î  Bi 4.  +,-!!! ()*+;*+7*@+1# ABACA! 7x 5y 8 0,+ - =  9x 3y 4 0,- - =  x y 2 0+ - = 7; )*)+ !)- %&'  AB : x y 0, AC : x 3y 8 0, AH : 5x 7y 4 0- = + - = - + =  Bi 5. .%&&'() ()*+#7 ( ) BH : x y 1 0+ - =  ( ) CK : 3x y 1 0- + + =  !; ( ) BC : 5x y 5 0- - = 27;> A;27 !)DE %&'  AB : x 3y 1 0, AC : x y 3 0, AL : x 5y 3 0+ - = - + = + - =  Bi 6. #/0)123 ()*+# ( ) A 1;3  !A! x 2y 1 0- + =  ! y 1 0- = 7;27E %&'  AB : x y 2 0, AC : x 2y 3 0, BC : x 4y 1 0- + = + - = - + =  Bi 7. 4 7F ( ) ( ) A 1;2 , B 1;2-  !4#  ( ) d : x 2y 1 0- + = -G2F+4H:F )*+;!7 !IG7J.5H 1, CA CB=  2, AB AC=  %&'1, 1 C 0; 2 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø 2, ( )   1 2 C 3;2 C ; 5 5 æ ö ÷ ç ÷ Ú - ç ÷ ç ÷ ç è ø  Bi 8. 5673+,- ()*+ !F ( ) M 1;1- A!F2)*- ;)+ !*+KLMN? 2x y 2 0+ - =  ! x 3y 3 0+ - =  1,678:9)*+2()*+ ! +- 2,3453()*+ %&'1, ( ) ( )   3 4 A 1;0 , B 3;2 , C ; 5 5 æ ö ÷ ç ÷ - ç ÷ ç ÷ ç è ø  ! CH :10x 5y 2 0- - = 2, ( )  ABC 6 S vdt 5 D =  Bi 9. .89:  $5< x y 1 0+ - =  ! 3x y 5 0- + = -G453:!#;N?G 9A!F2# !F2OA! ( ) I 3;3  %&' ( )  ABCD S 55 vdt=  Bi 10. 7;+,-:  $5<%J7)*+#9 ( ) A 2; 3 ,- ( ) B 3; 2-  !4537)*+:N 3 2 *=P2()*+  d : 3x y 8 0- - = F+ %&' ( ) ( )  C 1; 1 C 4;8- Ú  Bi 11. +,<=>?@;3A5B  $5<QKHK "#()*+:9 ( ) A 3;9  !7*R+SABACA! 3x 4y 9 0,- + = y 6 0- = )Q27G %&' AD : 3x 2y 27 0+ - =  Bi 12. @C<D3)EF>?@;3@CGD  $5<QKHK "#()*+#9 ( ) A 0;1  !L7 T0* !+#LA! 2x y 1 0- - =  ! x 3y 1 0+ - = 3453()*+ %&' ( )  ABC S 14 vdt D =  Bi 13. +,-> +7)*+# ( ) ( ) ( )  A 6; 3 , B 4;3 , C 9;2- - -  U,7;2()*+ V,=72#)27)*+ W,FR?;)* !FS?;)+HRS,,*+ ! AM CN=  %&'U, AB : 3x y 15 0 AC : x 3y 3 0 BC : x 13y 35 0 ì ï - + = ï ï ï - - = í ï ï + - = ï ï î V, A d : y x 3= + W,  32 9 33 4 M ; , N ; 7 7 7 7 æ ö æ ö ÷ ÷ ç ç ÷ ÷ - ç ç ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø  Bi 14. HI>  $5< 1 : x y 1 0,D - + = 2 : 2x y 1 0D + - =  !F ( ) P 2;1  U,FX !F@2( U  ! ( V  V,FX !Y( U ( V ABAC; F)*HXA!F)* %&'U, y 1 0- = V, d AB : 4x y 7 0º - - = Z#F[KW7\ Bi 15. #>  $5<QKHK "#F ( ) A 1;2-  ! ( ) B 3;4 F+? d : x 2y 1 0- + = H()*+ "]+ %&' ( )   3 4 C 3;2 C ; 5 5 æ ö ÷ ç ÷ Ú ç ÷ ç ÷ ç è ø  Bi 16. #J#$K0.%&4+,1>  $5< d : 2x 3y 1 0+ + =  !F ( ) M 1;1 27FR !; $4 # 0 45  %&' x 5y 4 0- + = +#F[K7 Bi 17. #J#$K0.%&4+,->  $5<QKHK "#F ( ) A 3; 1-  ! ( ) B 3;5 -G F ( ) I 2;3-  !7JF) * %&'  x 2 0 x 5y 13 0+ = Ú + - =  Bi 18. >  $5<QKO()*+ $ AB : x 2y 7 0- + = 7 ./0)*ABAC# x y 5 0+ - =  ! 2x y 11 0+ - =  -G34532()*+ !A^)+ !*+ %&' ( )  ABC 45 S vdt 2 D =  ! AC :16x 13y 68 0, BC :17x 11y 106 0+ - = + - =  Bi 19. +,?0L@;3A5B>  $5<QKHK "#()*+:9 ( ) A 3;9  !7*R+SABACA! : 3x 4y 9 0- + =  ! y 6 0- = )Q %&' AD : 3x 2y 27 0+ - =  Bi 20. .%&45>  $5<QKHK "#()*+ ";) $ ( ) ( ) B 3;0 , C 7;0 ,- :7.3> r 2 10 5= - =@2 >()*+:F@#!4 %&' ( ) ( )    I 2 10; 2 10 5 I 2 10; 2 10 5+ - Ú - -  + )#J>  $5<:F ( ) ( ) ( )  A 2;1 , B 2;3 , C 4;5- -G  77J:F)*+ %&'D!7:()*+ MN : x 3y 6 0 NP : x 2y 9 0 MP : 2x y 2 0 ì ï - + = ï ï ï + - = í ï ï - + = ï ï î  + +,-=1M R#'OA! x 2y 7 0+ - = ;# A! x 3y 3 0+ - = 9A! ( ) 0;1 7;2 + #M  $5<F 5 M ;2 2 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø  ! ( ) 1 : x 2y 0D - =  ( ) 2 : 2x y 0D - = D^4RY ( ) ( ) 1 2 ,D D  ABAC;)*HRA!F2;)* + 568+,-=1M  $5<()*+# ( ) A 1;3  ! _70* !+ABAC#' x 2y 1 0- + =  ! y 1 0- = -GA^ 7;2()*+ %&'  AB : x y 2 0, BC : x 4y 1 0, CA : x 2y 7 0- + = - + = + - =  +  M  $5<()*+#F ( ) A 1;2  *R !=7+QL# 2x y 1 0+ + =  x y 1 0+ - = -G *+ %&' BC : 4x 3y 4 0+ + =  + 1JNM  $5< 7;2()*+:9 ( ) A 4; 1 ,-  ! T`9AB ACA! 1 d :2x 3y 12 0- + =  ! 2 d : 2x 3y 0+ =  %&'  AB : 3x 7y 5 0, AC : 3x 2y 10 0, BC : 9x 11y 5 0+ - = + - = + + =  + #J#$K0OBM  $5<()*+#9 ( ) A 1;3 ,   BH : 2x 3y 10 0- - =  ! BC : 5x 3y 34 0- - = 678 79* !+ %&' ( ) ( ) B 8;2 , C 5; 3-  + +,M  $5<QKHK "# ( ) ( ) A 1;2 , B 5;4-  !  : x 3y 2 0D + - = FR? D H MA MB+ uuur uuur  Y_ %&' 5 3 M ; 2 2 æ ö ÷ ç ÷ - ç ÷ ç ÷ ç è ø  + PQ+,-M  $5<QKHK "#()*+#F ( ) A 2; 1-  !=72#*+ABAC# ( ) B : x 2y 1 0,D - + =  ( ) C : x y 3 0D + + = ;*+ %&' BC : 4x y 3 0- + =  + @%1R+,-=1M  $5<QKHK "#()*+ "])*  ( ) ( ) A 3;5 , B 7;1  !*+F ( ) M 2;0 9+ %&' ( ) C 3; 1- -  + +,-M  $5<QKHK "#F ( ) ( ) A 1;1 , B 2;1 ! d : x 2y 2 0- + =  1,+LINF)*] J`324 2,FR4Ha.[7 ( ) MA MB+ :O_ %&' 23 16 M ; 15 13 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø  + FCS+,-M  $5<()*+# ·  0 AB AC, BAC 90= = * ( ) M 1; 1- A!F;*+ ! 2 G ;0 3 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø A!=2()*+9)* + +  @(568+,-=1M  $5<()*+#9 ( ) A 3;0  !  ( ) BB' : 2x 2y 9 0+ - =  ! ( ) CC ' : 3x 12y 1 0- - = 7; 27)*+ +  +,<=M  $5<QKHK "#()*+# ( ) A 2; 4 ,- ( ) B 0;2  !F+' 3x y 1 0,- + = 453()*+:N 1 Z 845 3\-GF+ %&' ( )   1 1 C ; C 1; 2 2 2 æ ö ÷ ç ÷ - - Ú - - ç ÷ ç ÷ ç è ø  + #J?#$K0.%&4+,-T  $5<QKHK "#:F ( ) A 1;2 , ( ) B 3;1 ,  ( ) C 4;3 +LN()*+A!7=7 27# %&'  AH : x 2y 5 0, BI : 3x y 10 0, CK : 2x y 5 0+ - = + - = - - =  + U9F<VW,+,-T  $5<QKHK "#7# 9A! ( ) A 4;3 ,  !9.7# ABACA! 3x y 11 0- + =  ! x y 1 0+ - = -G 7; 7 %&'  AC : x 3y 13 0, AB : x 2y 2 0, BC : 7x y 29 0+ - = - + = + + =  + .5KH444&'()+,-T  $5<QKHK "#)*+Q# ; !OA! AB : 7x 11y 83 0,- + = CD : 7x 11y 53 0,- - =  BD : 5x 3y 1 0- + = * !Q O)+bH2) !+ %&' ( ) ( ) AC : 3x 5y 13 0 A 4;5 , C 6; 1+ - = Þ - -  + 1.N+,-T  $5<QKHK "## '  1 2 d : 2x 3y 1 0, d : 4x y 5 0- + = + - = P)A!F24 U  !4 V  F*?4 U  !F+?4 V H()*+#=A!F ( ) G 3;5  %&' ( )   61 43 5 55 A 1;1 , B ; , C ; 7 7 7 7 æ ö æ ö ÷ ÷ ç ç ÷ ÷ - ç ç ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø  + #J#6K0OB+,-T  $5<QKHK "#()*+ $ ( ) A 2;1 , ( ) B 4; 3-  ! ( ) C m; 2- %8F()*+ ";+ %&'  m 1 m 5= Ú =  + @%8V3&'()T  $5<QKHK "#4#  x y 3 0+ - =  !F ( ) ( ) A 1;1 , B 3;4- FR 4H.[70R)*:NU %&' ( ) ( )  M 0;3 M 10; 7Ú -  + #J?.%&'()+,<T  $5<QKHK "#()*+ "=; ( ) A 4;1  !;J*+#' 3x y 5 0- + = ; # ")+ !)* %&' AC : x 2y 2 0- - =  ! AB : 2x y 9 0+ - =  + 1SX3T  $5<QKHK "# ( ) A 1;1 ,-  ( ) B 4;3-  F+ x 2y 1 0+ + = H.[70F+ )*:Nc %&' ( )   43 27 C ; C 7;3 11 11 æ ö ÷ ç ÷ - Ú - ç ÷ ç ÷ ç è ø  + 5+,T  $5<QKHK "#()*+: ( ) C 2; 4 ,- -  = ( ) G 0;4  ! ( ) M 2;0 A!F;*+-G  L;)* %&' AB : 4x 5y 44 0+ - =  + #$K02T  $5< d : 3x 4y 1 0- + = -G  HH $4 !#.[74:NU %&'   1 2 : 3x 4y 4 0 : 3x 4y 6 0D - - = Ú D - + =  + #J&'()"  $5<QKHK "#  1 2 d : x y 1 0, d : 2x y 1 0+ + = - - =  !F ( ) M 2; 4- ( @ !Y4 U 4 V ABAC;) !*!@A!F2)* %&' AB : x 4y 14 0D º + - =  + #J@," ()*+*F ( ) B 4; 1 ,- )-# A! : 2x 3y 12 0,- + = )R# : 2x 3y 0+ =  7L7;27)*+ %&' ( ) ( ) ( )  A 3;2 , B 4;1 , C 8; 7- -  + U9F<VW," 7;2()*+:9 ( ) A 1;1 ,  ! 9*ABAC#' 3x 4y 27 0, 2x y 8 0+ - = + - =  %&'  AB : x 1, AC : x 2y 1 0, BC : x 8y 49 0= - + = + - =  + .%&V3Y"  $5<QKHK "#()*+#9 ( ) A 2; 7 ,- +R*1#ABACA! x 2y 7 0+ + =  ! 3x y 11 0+ + = 7)+ !*+ %&' AC : x 3y 23 0- - =  ! BC : 7x 9y 19 0+ + =  + +,-=1=<*  $5<F)<! !F* <H) !*dL $ d : x 2y 3 0- + =  %&' ( ) ( ) A 2;0 , B 0;4  + -=1=<ZBSB1H[  $5; d : x y 3 0+ + =  F ( ) A 2; 4-  !; $4#:N 0 45  %&'   1 2 : y 4 0 : x 2 0D + = Ú D - =  + -=1=<ZBS9[  $5;7)*+#7;A!  AB : x 3y 7 0, BC : 4x 5y 7 0, CA : 3x 2y 7 0+ - = + - = + - =  ./09)27)*+ %&' AH : 5x 4y 3 0- + =  + @;3?#0J?)?.%&&'()!""  "#G  F2 : 3x 5y 2 0,- + =  5x 2y 4 0- + =  !HH $ 2x y 4 0- + =  %&' d : 38x 19y 30 0- + =  + @;3/<\3/&'()!""  "#GA^=72#` ;:]  1 2 : 3x 4y 12 0, :12x 3y 7 0D - + = D + - =  %&' ( ) ( ) d : 60 9 17 x 15 12 17 y 35 36 17 0- + - - + =  + @;3]^&&'()+,1!"*  "#4 U  !4 V ABAC# '  1 2 d : x y 1, d : x 3y 3 0+ = - + = -G 4dL $ 4 V 4 U  %&' d : 3x y 1 0- + =  + @;3/<\3/&'()!"*  "#7=Xef:; 7 PQ : 2x 3y 5 0,- + = ;:? PR : x y 1 0+ + = ;:?ef: N#F ( ) D 1;1  %&' RQ :17x 7y 24 0+ - =  + @;313#?@;3]^&&'()!"!  "# ( ) 2 C : y x 9= +  !  d : ax 5y 32 0- - =  1,TG 2,3.[7g0FR`h24K !2R 3,3.[7Y_i ! %&'1,T ( ) 2 2 2 2 x y H : 1 3 3 - = - ]?2, 2 4x 5 x 9 32 z 41 - + - = W, 16 M 4; 5 æ ö ÷ ç ÷ - ç ÷ ç ÷ ç è ø  + @;3_??<^3&'()!*  "#G F ( ) A 1;2 !.[70F ( ) M 2;3  !F ( ) N 4; 5- _:N %&'  d : 3x 2y 7 0 d : 4x y 6 0+ - = Ú + - =  + ;35%9&'()!! QKHKH "#()*+#9 ( ) A 2;2 D^ 7;2()*+*N7 9x 3y 4 0- - =  ! x y 2 0+ - = AB ACA!727_70* !+ %&'  AC : x 3y 8 0, AB : x y 0, BC : 7x 5y 8 0+ - = - = + - =  + @;3OB!!:?@;3H!!M?9@1 _J &'()!!"?;35%#. D^7;27)*+: ( ) B 2; 1 ,- ) ! =7#+#ABACA! 3x 4y 27 0; x 2y 5 0- + = + - =  %&'  AB : 4x 7y 1 0, BC : 4x 3y 5 0, AC : y 3+ - = + - = =  8L`S X x 2y 5 0+ - = A!=7!2# +."[A!=7#+%J37R Hd%;GJ!FFH!."75jk="Ga A;=7!#+A! x 2y 5 0+ - =  ![.[? + 9@1 _J&'()!!:  "#F ( ) P 2;5  ! ( ) Q 5;1 D^ X7f;#4!:N 3  %&'  d : x 2 0 d : 7x 24y 134 0- = Ú + - =  + @;3&8)&'()!!>  $5<QKHK "#:'   1 2 3 d : 3x 4y 6 0, d : 4x 3y 1 0, d : y 0+ - = + - = = P  1 2 2 3 A d d , B d d ,= Ç = Ç  3 1 C d d= Ç  1,=72#)2()*+ !3453 ()*+ 2,>()*+ %&'1, A d : x y 1 0+ - =  ! ( )  ABC 21 S vdt 4 D =  2, 2 2 2 73 9 1 73 73 1 x y 8 8 8 æ ö æ ö æ ö ÷ ÷ ÷- - - ç ç ç ÷ ÷ ÷ ç ç ç - + - = ÷ ÷ ÷ ç ç ç ÷ ÷ ÷ ç ç ç ÷ ÷ ÷ ç ç ç è ø è ø è ø  + @;3]^&&'()+,-=1!!>  "#4 U  !4 V ABAC# ' 1 d : kx y k 0,- + =  ( ) ( ) 2 2 2 d : 1 k x 2ky 1 k 0- + - + =  1,+LN..a4 U A"Fd8 2,$l78.G78F24 U  !4 V  3,m32F#..a %&'1, ( ) o M 1;0- 2, 2 2 2 2 1 k 2k M ; 1 k 1 k æ ö - ÷ ç ÷ ç ÷ ç ÷ ÷ ç + + è ø  3,%>' 2 2 x y 1+ = A; ( ) o M 1;0-  [...]... nm 1997 Trong mt phng toa ụ Oxy, cho ng thng d co phng trinh 3x + 4y - 12 = 0 1/ Xac inh toa ụ qua cac giao iờm A, B cua d lõn lt vi truc Ox, Oy 2/ Tinh toa ụ hinh chiờu H cua gục O trờn ng thng d 3/ Viờt phng trinh ng thng d' ụi xng vi d qua O S: 1/ A ( 4;0) , B ( 0;3) + ổ 48ử 36 ữ ỗ 2/ H ỗ ; ữ ữ ỗ25 25ứ ữ ố 3/ d' : 3x + 4y + 12 = 0 ai hoc An Ninh ờ 2 khụi D nm 1997 Trong mt phng toa ụ cho iờm A... vi ng cong ( C) cụ inh khi m thay ụi S: d : y = + 1 m m2 x, luụn tiờp xuc vi parabol ( P ) : y = x2 8 4 8 ai hoc Huờ khụi D nm 1997 Trong mt phng toa ụ Oxy, cho hai ng thng D 1 : 4x - 3y - 12 = 0, D 2 : 4x + 3y - 12 = 0 1/ Tim toa ụ cac inh cua tam giac co ba canh lõn lt nm trờn cac ng thng 1, 2 va truc tung 2/ Xac inh tõm va ban kinh ng tron nụi tiờp cua tam giac noi trờn S: 1/ A ( 0;- 4) , B ( 0;4)... c, tim D sao cho ABCD la hinh binh hanh Tinh diờn tich hinh binh hanh S: 1/ C ( - 3;- 1) + ; 2/ D ( - 1 - 3) va SY ABCD = 12( vdt) ai hoc Cõn Th nm 1998 ; Trong mt phng toa ụ vuụng goc Oxy, cho ABC co inh A ( - 1 - 3) 1/ Biờt ng cao BH : 5x + 3y - 25 = 0, ng cao CK : 3x + 8y - 12 = 0 Tim toa ụ inh B, C 2/ Biờt ng trung trc cua AB la D : 3x + 2y - 4 = 0 va trong tõm G ( 4;- 2) Tim toa ụ inh B, C... d : 3x + 3y - 8 = 0 ù ù AB ù ớ S: 1/ ù dAC : 9x - 3y + 3 = 0 ù ù d : 15x - 21y + 41 = 0 ù BC ù ợ + 2 2 ổ 17ử ổ 5 ử ổ 9ữ 185 ử 5 ữ + ỗy - ữ = ỗx ữ ỗ ữ ỗ 2/ ( C) : ỗ va G ỗ ; ữ ữ ỗ ữ ỗ9 9 ữ ữ ỗ ữ ố ứ 12 ố 4ữ 72 ố ứ ai hoc Giao Thụng Võn Tai Tp Hụ Chi Minh ờ 1 nm 1998 ;2 Trong mt phng toa ụ Oxy, cho hai iờm A ( - 1 ) va B ( 3;4) Tim toa ụ iờm C trờn ng thng: x - 2y + 1 = 0 sao cho ABC vuụng C ổ 4ử... toa ụ vuụng goc Oxy, cho iờm P ( 3;0) va hai ng thng: d1 : 2x - y - 2 = 0 va d2 : x + y + 3 = 0 Goi d la ng thng qua P va ct d1,d2 lõn lt A va B Viờt phng trinh cua d biờt rng PA = PB S: d : 4x - 5y - 12 = 0 d : 8x - y - 24 = 0 + ai hoc Vn Lang khụi B, D nm 1998 Trong mt phng toa ụ vuụng goc Oxy, cho ABC co inh B ( 3;5) , ng cao ke t A co phng trinh: 2x - 5y + 3 = 0 va ng trung tuyờn ke t inh C co... hinh vuụng co hai canh song song i qua A va C va hai canh con lai i qua B va D S: 1/ SABCD = 6( vdt) + ỡ MN : 7x + y - 15 = 0 ỡ MN : x - 3y + 1 = 0 ù ù ù ù ù ù ù PQ : 7x + y - 26 = 0 ù PQ : x - 3y + 12 = 0 ù ù ớ ớ 2/ ù NP : x - 7y + 7 = 0 ù NP : 3x + y - 1 = 0 ù ù ù ù ù ù ù MQ : x - 7y - 4 = 0 ù MQ : 3x + y + 10 = 0 ù ù ù ù ợ ợ ai hoc Y Dc Tp Hụ Chi Minh hờ C nhõn nm 1997 Cho ABC, canh BC co trung... ( 4;0) + 2/ B ( 5;1) , C ( 8;- 4) ai hoc Vn Hoa Ha Nụi nm 1998 Trong mt phng toa ụ vuụng goc Oxy, cho ABC biờt inh C ( 4;- 1) va ng cao, ng trung tuyờn ke t mụt inh co phng trinh lõn lt la 2x - 3x + 12 = 0 va 2x + 3y = 0 Tim phng trinh cac canh cua tam giac ABC S: AC : 3x + 7y - 5 = 0, BC : 3x + 2y - 10 = 0, AB : 9x + 11y + 5 = 0 + ai hoc Huờ khụi D nm 1998 Trong mt phng toa ụ vuụng goc Oxy, hay... - b2 x + ay = b vi b2 = 4a2 + 1 1/ Xac inh giao iờm cua d1 va d2 2/ Tim tõp hp ( E ) cac giao iờm cua d1 va d2 khi a, b thay ụi ổ 1 aử ữ Mỗ S: 1/ ỗ- ; ữ ữ ỗ b bứ ữ ố + 2/ Ellipse ( E ) : x2 y2 + =1 2 12 ổử ỗ1ữ ỗ ữ ữ ỗ2ứ ố ữ ai hoc a Nng khụi A ai hoc Kinh Tờ Tp Hụ Chi Minh nm 1999 Trong mt phng toa ụ vuụng goc Oxy, cho hai ng thng d1 : 2x - y - 2 = 0 va d2 : 2x + 4y - 7 = 0 1/ Viờt phng trinh ng... B 2/ Gia s M di ụng trờn ng thng ( D) : x + y - 2 = 0, tim quy tich iờm B Hay xac inh M ờ ụ dai canh AB la ngn nhõt uu ur uu ur ỡ ù MA = 3MG ù uu ị ur ớ u S: 1/ ù uur ù CB = 2CM ù ù ợ + ỡ ù ù A ( - 4 ;12) ớ ù B( 6 ) ;4 ù ù ợ ổ 1 9ử ữ ỗ 2/ Quy tich la d : x + y - 10 = 0 va M ỗ- ; ữ ữ ỗ 4 4ứ ữ ố ai hoc Giao Thụng Võn Tai khụi A nm 2001 Trong mt phng vi hờ truc toa ụ Descarter vuụng goc Oxy, cho hinh... inh C S: Ba canh ABC ụng quy tai M ị Vụ li ị Bai toan khụng xac inh ị $C thoa yờu cõu bai toan + ai hoc Nụng Nghiờp I nm 2001 ;1 Trong mt phng Oxy cho iờm A ( 1 ) va ng thng d co phng trinh: 4x + 3y = 12 1/ Goi B va C lõn lt la giao iờm cua d vi cac truc Ox va Oy Xac inh toa ụ trc tõm cua ABC 2/ iờm M chay trờn ng thng d Trờn na ng thng i qua hai iờm A va M, lõy uu uu u r ur iờm N sao cho AM.AN = 4 . "#GA^=72#` ;:]  1 2 : 3x 4y 12 0, :12x 3y 7 0D - + = D + - =  %&' ( ) ( ) d : 60 9 17 x 15 12 17 y 35 36 17 0- + - - + =  + @;3]^&&'()+,1!"* . #$%&'()!!* ' ( ) 1 : 4x 3y 12 0D - - =  ! ( ) 2 : 4x 3y 12 0D + - =  1,678927#:; ( ) ( ) 1 2 ,D D . @;3J+,<!!"  1 : 4x 3y 12 0,D - - = 2 : 4x 3y 12 0D + - =  1,7927#:;ABACN?7( U ( V 

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