Tài liệu ôn thi THPT quốc gia môn Toán - Chuyên đề 8: Hình phẳng Oxy

VD 213. Trong mặt phẳng tọa độ Oxy , cho hai đường thẳng 1 : 3 0 d x y + = và 2 : 3 0 d x y − = . Gọi (T) là đường tròn tiếp xúc với d1 tại A, cắt 2 d tại hai điểm B và C sao cho tam giác ABC vuông tại B. Viết phương trình của (T), biết ∆ABC có diện tích bằng 3 2 và điểm A có hoành độ dương. Đáp số: 2 2 1 3 ( ) : 1. 2 2 3 T x y     + + + =         VD 214. Cho 2 2 1 ( ) : 4 C x y + = , 2 2 2 ( ) : 12 18 0 C x y x + − + = và đường thẳng : 4 0. d x y − − = Viết phương trình đường tròn có tâm thuộc 2 ( ), C tiếp xúc với d và cắt 1 ( ) C tại hai điểm phân biệt A và B sao cho AB vuông góc với d. Đáp số: 2 2 ( ) : 6 6 10 0. C x y x y + − − + = VD 215. Cho các đường tròn ( ) 2 2 1 1 ( ) : 1 2 C x y − + = và ( ) ( ) 2 2 2 ( ) : 2 2 4. C x y − + − = Viết phương trình đường thẳng d tiếp xúc với đường tròn 1 ( ) C và cắt đường tròn 2 ( ) C tại M, N để 2 2. MN = Đáp số: : 2 0 : 7 6 0 MN x y MN x y  + − =  + − =  hoặc : 2 0 : 7 2 0 MN x y MN x y  − − = ⋅  − − = 

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C O $% > " $%D02'(* Z$ +( =A ?! - - / 2  - 2  - . 2  - 1 2 - 3 . 3 2  - . 3 . 2  - 3 . 0/ 2  - . 3 /4 2 ( 6 Z 7 Z 6 ( 7 ( 6 7 Z 6 7 Z 6 7 ( 6 7  + = = − = + = ⋅ + + = − + = + − = − − =    0@ H+d  ': > ; <=kL5 +   C O ZT[eK&[T = ; r     )+ - . 3 /8 2 6 7+ − = ]!^  <=!*    C  O P +% D%!Q"   J=   !ZTe%D/ ?! - ( ) ( ) ( ) ( )34   2 4   2 3   3 3  (  Z− − −    0 T +   C O  (Z $ - 0 / 2( 6 7− + =   )+ - 4 /3 2(Z 6 7− + =      & 0/9 H <=!*    C O h ?! - 0/ /. /3 /0 . 0     3 .   1 1 1 1  (  Z     ⋅           0. H+ > ; <= 67   +   C O  (Z $ A / 2  0              - 0 0 2( 6 7− + = '($ 0 ( Z= H <=!*  (Z %  26 <  ?! -  02  0 0  .2   / 0 (  Z− − −    0/ H+ > ; <= 67  +   C O  (Z $!        e( (   FGF ,   !& 3 1  8 1  1 0  0/9        ( %  /8(Z: =  ?! - - / 2( 6 7− + =  +d - . // 2( 6 7− + =  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123&2   00 H+d  ': > ; <= 67  +   C O  (Z %  0 ( (= ?   (  & 3 /  . 9   −       (  & 2 .    Z   & / 3  .   −       Z   8 0     !  (Z  ?! - - . /4 /. 2 - /4 . U 2 ( 6 7 ( 6 7  + − =  − + =  +d - . U /. 2 - U . . 2 ( 6 7 ( 6 7  − + = ⋅ + + =    07 T +   C O  (Z $     - 0 / 2( 6 7− − =      )+ F( - 4 /3 2(Z 6 7− + = & 0/9 D B  )+  H <=&  h ?! - /2    0: H+d   67  +   C O  (Z $ A 1 .  0 0        '(=(  )+%D 08 ?    ( Z FGF ,  !& 0 .   / 09  − H <=&  h ?! - 2/  +d 4 /U  1 1    ⋅       0; H+d   67  +   C O  (Z $ 0 ( Z=   - / 2( 6 7− + = g<  F(& B Z + + .  Z= & / /  0 0 9       F(  &  ( Q +R !  S& (     %D 3 H  ?! - /88 /88  / 3 3    + ⋅         0< H+d   <= 67  +   C O  (Z $*  / - 0 0 2( 5 6 7∈ − + = *  0 - 1 2 5 6 7∈ − − = g< F(     ( L   )+  [  U 0    U 0 1 1 9 [        FGF , F(  &  '( Z H        (  Z %  36 >  ?! - /2  / 3  U 3  U2 (  Z    0? H+ d   < = 67   +    C  O  (Z  $ 2 0  g<  F(      ' E$ (  FB  HB  (  Ff5& W + + (W = [       - 2ZW 6 7− = H     (  Z %  8(Z: = '( 2(7 >  ?! - 2 1  0 1  0 0(  Z  +d . 0  2 .  0 0(  Z    K2L MN4O  BC.: H+d   <= 67  +  ' E (Z $& 0 3(   &  Z  F(  /2W − '( 0 /X − F(  &  Z H <=!* JF  ' Eh ?! -  0 0  32  2 0 ( Z− −  BC.; H+d   <= 67  +  ' E (Z $ A / U  0 0    − ⋅    K*    ( FG F , D B    / - . 3 6 25 6 7+ − = '( 0 - . 3 / 25 6 7+ − = H        (  Z  ?! -  3 1   //  . 3  26 03 .0 U. 48 3U /U0 86 /3U Z           01 01 01 01 01 01 01 01  (  Z (  Z  − −  ⋅        − −                 www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123%2 BC.< H+d   <= 67  +   C O  (Z $  ./  - 0 1 2  5 6 7− ∈ − − = g< W  F( + & M     J A (  %! Q"  (Z  ':    Z  K    ' E$ Z L    (W F( 8 0 − H <=    (  Z h ?! -  0 0  4/  8 3(  Z− −  BC.? H+d   67   +  ' E (Z $ . 3( '(  )+ - 0 2 6 7− + =  H <=!* JF  ' Eh ?! - 0 3  . 1  0 1  Z  +d . 1  0 3  0 1  Z  BC/@ H+d   67  +   C O  (Z $  08 − *  - 0 8 2( 5 6 7∈ − + = g<  9   FG F ,  F( & B     ( Z  + + (9 (   = ⋅ [  9 '( (  #     & 0 /1  1 1    ⋅    H <=& 9 h ?! - / 09  BC/ H+d   67  + &  // .  U 4 (− − NO      + +': ( '(#   J Q"  (   & A%>     Z 9':       '( Z  B (  + ( =   ' Eh ?! - - 0 1 /2 1 25 6 7+ + ± =  BC/. H+d   <= 67  +  ' E (Z $ A  $ +( =%D U 0 '(D B   - . 25 6 7− − =   &  ( F(+& 5 ': ; +(  H <=!*   ' Eh ?! - U U . . U . /1 .        0 0 0 0 0 0 0 0  (  Z         −                 +d /1 . U . . . U U        0 0 0 0 0 0 0 0  (  Z         − ⋅                 BC// H+d   <= 67  +   C O  (Z $ - 0 / 2Z 6 7− + = & 0 .9  D B   ( &  // − D B   ( H <=  (  '( '       Z %  9 Z⊥  ?! - // /. /. U /4 0 0/       - 0 2 1 1 1 1 1 (  Z 6 7     + + ± =         BC/0 H+d   <= 67  + / 0 .- . 2  - 0 1 2  - 25 6 7 5 6 7 5 6 7− = + − = − = H <=! & / 0  5 ( 5∈ ∈ '( .  Z 5∈ + + (Z F(  ' Eh ?! - . / / /    0/  //   0 0 0 0  (  Z              +d /1 1 1 1 1 /1 /1    2       3 3 0 0 0 3 3  (  Z         ⋅                 BC/7 H+ d   < = 67   + 0 .  1 0  68 (   H & - . 2Z 5 6 7∈ − + =  &  ' E 9  $!       9   9  !&       (  Z + +> "  9   ! ^F: f h ?! - 4/2Z  +d  04 03Z − −  BC/: H+d   <= 67  +   C O  (Z $*   / .Z −   A! +$Z( $   F( 8 26 7− + = H ( %  /6(Z: = '(  6 7=  ?! -  . 8( − −  +d  ./0( −  BC/; H+d   <= 67  +  ' E (Z $ A //   0 09 − ∈   ( '( & 0 0 − ∈   Z ]!^  <=!*   ' Eh ?! - / 1   ./  / .  1/ (  Z− −  +d  ./  / 1  1/  / . (  Z− −  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   012332 BC/< H+d    " %D 0 0 g<  9   FGF , F(  & ( '( Z %  2/  - 0 0 3 29  6 7+ − = H <=  h ?! -  02  +d 0 6  . .    ⋅       BC/? H+d   <= 67  +  ' E (Z $ A / / − g< 9  F(& B   Z  ` 0 9 9Z= H <=        (  Z %  - 0 1 29 6 7− − =  ?! - / .   / /  //  . / (  Z− − − − '(F(  I + . 3 28 + =  BC0@ H+d   <= 67   +  ' E (Z  $ - 3 2 5 6 7∈ − − =  32 9 (∈  & 2 0 Z∈ + + 9∆ A   H <=!*   ' Eh ?! -  / 1  1 .  . .   ./ (  Z− − − − '(F(  I': . 2 8+ =  BC0 H+d   <= 67  +   C O  (Z $ - . 4 2 5 6 7∈ + + = '( / 1  g< 9 F(&D B   ( + + 0 9 (=   F(    ' E$  (  B   9Z H  (  %  1 /  0 0    − ⋅     ?! - 1 /  0 .( − −  BC0. H+d    " %D 8 '(      )+ - 0 U 2 6 7+ − = ?   (  & 1 19    Z   & 1/ H <=!*    C O  (Z  ?! - . .  3 3  4/  82 . .  0 0   / 1  28  (  Z  (  Z   − '(F(  I':   ,  ./ 4  1 1    ⋅     BC0/ H+d   <= 67  +  ' E (Z $  ( Z 6∈ '( / - 2 5 6 7∈ − = & 0 - 0 / 2 5 6 7∈ + − = H <=!*   ' Eh ?! - //  22  / /  02 (  Z−  +d //  02  / /  22 (  Z−  BC00 T +  ' E (Z  $ A / /    0   - 0 4 2 9 Z 9 9Z 9 6 7− ∈ = − + = H <= !*   ' E (Z h ?! -  4 4   14  U 1  4 U (  Z− − − −  +d  4 4  4 U  U 1   14 (  Z− − − −  BC07 H+ d    "  %D /8  '( *   / 0 − − H <=!* JF   C O  (Z %   J+     C O  (Z $   F( 0 0  -  0  / /2 6 7+ + − = '( 2(6 >  ?! - /2   . 3   1 0(  Z− −  BC0: H+d    "  3 '( A . /  32 (−  g< [ F(&D B Z &$C   ([ '( Z %D α ': 0 1 + 1 α = ⋅  H  ?! - 3 0  02  0 0  Z− − '(F(  IQ  (Z[ F(  %  (  BC0; H+d   <= 67  +  ' E (Z $  / 0Z − g< 9 F(  & ( '(  F(& B   + + /  3   =   - / 29 6 7− + = H <=! * JF  ' E%  296 >  ?! - / 0 4 8 . /3        1 1 1 1 1 1  (        −            '(F(  IQ  0 2 8+ =  BC0< H+d   <= 67  +  ' E (Z $ / 09 F(  &  (  r       5Qj S   Z9∆ F( - 1 / 25 6 7− + = H ( %  26 >  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123<2 ?! - . 1  0 0 (        +d . 0/  /2 /2 (   ⋅     BC0? H+ d   67   +    C  O  (Z  $ 0 1(Z: =  '( =     J 0 0  -  0  / / 6 7− + + = ?  )+ - 0 / 2 5 6 7⊥ − − = H ( %   6 6<  ?! - /2(  +d U 0  1 1 (   −     +d 0 1 1 /  / 1 1 (   ± − ⋅      ∓  BC7@ T +   C O  (Z $ 0   //( ( =  A / 2  0        H <=  ( Z h ?! - / /  2/( Z−  +d . / 6 /     1 1 1 1 ( Z     − − ⋅         BC7 T +   C O  (Z $ /8 /0 - / 2   1 1 Z 6 7 9 (Z   − + = ∈    '(  &  Z  F( & 8 1 H <=!*    C O  (Z h ?! -  /2  / 0  4 3  18 (  Z− −  BC7. T +    C  O  (Z  $ .  - 0 U 2   3 1   / 0 (Z:  6 7 9 (  Z= + − = − ∈ ∈  H <=*   % *   $ +( =Ah ?! -  0 0 . 8 0 ± − ∓  BC7/ T +   C O  (Z  $ / 0- 0 0 2  - 1 2( 5 6 7  5 6 7∈ − + = ∈ − − = g<  F(      ( L   )+  '($ ( )U 0   U 0 1 1 9 [       FGF , F(  &  '( Z  H  ?! - /2  / 3  U 3  U2 (  Z   V   M Q RNJ S 1 1      7@ H+d    " %D3[  < =!*  /2  02 ( '(+&     )+  '( (Z D B   - 25 6 7− = KP5  <=!*   '( Z h ?! - . 3  0 3 Z  +d  1 3   8 3 Z− − − −    7 H+d   <= 67  +  %  (  (Z $ A 0 0 '(      L f  !  S= * $   F( 0 2 3 . 26 7 6 7− = − = H       (  Z h ?! - 0 3 22     3 3  8 6 1 1  (  Z   −       7. H+ d   < = 67   +   %  (  (Z  $ A 0 1 −  '(   A !$ ( $    0 3 26 7+ − = %  Z∆ $ < A / /3  . .    − −      < =!*   %  (  (Z h ?! - / 0  U 8  . /0   1 3 (  Z− − − −    7/ H+d   <= 67  +  %  (  (Z $ 88Z  / - 0 . /4 26 7∆ + + = F(     I+  Z '( 0 - 1 . 26 7∆ + − = F(  A!$ (  ]!^  <=!* JF  %  (  ?! - / 0  1 3   02 ( − −  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123V2   70 H+ d   < = 67   + (∆  $   + Qj S *  (  $    F( / 26 7+ + =  < Z  F( & LM       &   (  H <= ! *  ! (∆ %  <=& . 3Z '(  /2 − F( I A (∆ &  $ <= 5B'( =   0 8 26 7− − =  ?! - .2   /2   / 3 ( − − −    77 H+d    " %D/8[  (∆  A    3 ( = '( 0/ /6  1 1 [        F(    & ( L    H <=! *   %  (  (Z %  - . 2( 5 6 7∈ + − = n    ( 6 6 ∈  ?! - / 0  1 0(     7: FGHVIH+d   <= 67  +  %  (  (Z ?&  .29 − F(  &  ( & 2 / − F(    ' E$ (  B Z '( 3  . .         F( < A (Z∆ H <<!& ( '( Z h ?! -  0 .  02( Z−    7; H+d   67  +  %  (  (Z $ 1 /2(Z = g<    ' E $& Z FB!    ( ( FGF , F(  0 /9 − − '( 0 / − %   D B   - 4 25 6 7− = H <=    h ?! - 4 / 4 /     0 0 0 0       − − ⋅           7< H+ d   67   +   %  (  (Z  $ *  / 1(  <  F(      ' E$  FB ( '( - 0 0 2 6 7+ − =      A! +(  F( - /5 7 6= − H <=       Z  ?! - 3 /   3 1   / // ( Z− − − − −    7? H+ d   < = 67   +   %  (  (Z  $ 0/     )+ (Z  $    0 / 26 7+ + = ?& 9 D B   Z + + 9 =    - / 29 6 7+ − = H <=!* JF  %  (  (Z h ?! - ( )/ /.0   /0   6 4  0 0 ( Z      − − −           :@ H+d    " %D.*  0 . −  . 0 − '( < A (∆ F( - . 6 5 7 6∈ = −     !   %  (  ?! - - 4 3 08 2  - 6 8 2  - 4 3 0U 2  - 6 U 3. 2 - 0 / 2  - 0 / 2  - 0 3 2  - 0 3 2 ( 6 7 ( 6 7 Z 6 7 Z 6 7 ( 6 7 ( 6 7 Z 6 7 Z 6 7  − − = − + = − − = − − = ⋅ + − = + − = + − = + + =    : H+d   <= 67  +  %  (  (Z $  )+ - / 2 6 7− + =  & / 3 F( < A (∆ & 2 .W −  = +Qj S Z  Z∆ H < =!*   %  (  (Z %  .0Z: = '( 27 >  ?! - 18  /6   . 0  / 3 (  Z− − −    :. H+d   67   +  %  (  (Z  $ A  / . − '( < A (Z∆  F( & / 1  . .    ⋅        !   %  (  (Z % !   ( Z  F(    5Qj S*     J 0 0  -  .  . /2 6 7− + − =  ?! - - . 1 1 . . 2  - . 1 1 . . 2( 6 7 Z 6 7+ + − = − − − =  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   012342   :/ H+d   67  +  %  (  (Z $ (Z∆ ' E  Z K   ' E $ *   ( Z L   )+  FGF , F( 00 /3 /. //     1 1 1 1 [     ⋅        KP5  < =!*   %  (  (Z %  . 0(Z =  ?! - 6 3  0 3   //  1/ (  Z− '(F(  IQ  /8 0 /U 0.     1 1 1 1 ( Z     ⋅           K2L MN4O  BC70 H+ d   < = 67   +     / 26 7+ − =  '( . 1 26 7− + =  KP5  > "   %  ( $  D B   P += * F(+&    $'(+&   )+F( . .  ?! - ( )11 (Z: @>5 =  BC77 H+d   <= 67  +  %  (  (Z $  F( < A (Z∆       - 0 / 2Z 6 7− + =     - 1 . 0 2(Z 6 7− + = '( 2 0 H <= !*      ( Z   %  (  ?! - //  0 3   / / ( Z − −  BC7: H+ d    "  %D 3  *  0 0   0/ ( − [  A  F(+&   )+   (Z D B   - . 0 25 6 7− + = H <=  '( Z  BC7; H+d   <= 67  +  %  (  (Z $!*  2/  . 3 ( H < = ! *    Z   %  + &        )+ D B   (   %+F 0 /7 6= − + +> "   %  (  ! ^F: f h ?! - / 4 .   2 0 0  Z     − − ⋅         BC7< H+ d   < = 67   +   %  (  (Z  $ A / /  0    −          - . 1 2Z 6 7+ + =    (  & 8 09 '( , ':  Z =  $%D 31      ! JF  %  ( %  (Z (⊥  ?! - - 0 /2 2  - . /2 2  - 0 1 2( 6 7 ( 6 7 Z 6 7− − = + − = − + =  BC7? H+d   <= 67  +  %  (  (Z $ //  3 1 ( HA     %  (  =  - . 25 6 7+ + = H <=    Z %  U(Z: =  ?! -  0 8   1 /2 Z− − − −  +d .0 03 1. 10     4 4 4 4  Z     − − − − ⋅         BC:@ H+d   <= 67  + M! 9  ': ( ) ( ) ( )37/ 7.   3   3/   7./ . 9     −     '(& / /  0    −    H <=!&       (  Z FGF , D B!   9       9 + + (Z F(  %  (  O  F( A ?! - 0 0  32  2/   0 / (  Z− − −  BC: H+d   <= 67  +  %  (  (Z $ . / −    M (Z  '(   M  A!$Z FGF , F( 0 / 26 7− − = '( 7/ 26 = ]! ^  <=!* JF  %  (  (Z  ?! - / 0  1 .   / / ( Z − −  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   01232 BC:. H+d   <= 67  +  %  (  (Z $  8 8Z − − ?    I + Z $    / - 0 . /4 25 6 7+ + = '(  A!$ ( $    0 - 1 . 25 6 7+ − = H!* JF  %  (  (Z  ?! - / 0  1 3   02 ( − −   W   M Q RNJ S 1  J     :0 H+d   <= 67  +   A (Z $ !5   ( Z [     )+   (Z ' E$':  [  2 .  . 3 ( '(  D B ; +( ]!^  <=*  Z     (Z  ?! - 2 0Z −    :7 H+d   67   +   A (Z  $!5 F: F( Z  2 0   0 0 Z − − '( +&     (Z D B   3 26 7+ − = H <=!* JF   Q %  31 Z =  ?! - 0 0 0 0  0 3 0 0 3 0( + + + +  +d 3 . 0 0 0  3 3 0 0 0( + + + −    :: H+d   <= 67  +    (Z $ !5F(   ( Z *  2 3 −  32( H <=    Z %  (Z +    J 0 0  - 0 0 2 6 7 6 7+ − + =  ?! - / / / /     0 0 0 0  Z     − − ⋅           :; H+d   < = 67   +    (Z  ' E    '( Z  $ !5 F: Z     - . 2Z 6 7− =   - 0 2(Z 6 7− = $ 31(Z = '( 03(Z: = H <= *  ( % D& ( $ +( = h ?! - 6 /2 3 /2  1 1 (   ⋅         :< H+ d   < = 67   +    (Z  $  !5 F( (  '( Z  $ *  // '(  &  ( F( / 2 0 9   − ⋅    H <=*  Z $ +( = '( D B   \ - 1 / 25 6 7− + = % > "     (Z %D/3 ?! - 0//Z    :? H+d   <= 67  +   ' E (Z    '( Z $ 0 Z (= *  / 0( K   ' E$  S Z FB  F(&  /2 − g<  F(  &    H <=       Z %  - 0 0 2Z 6 7− − =  ?! - 4 . 2   12  / 6 0   Z     − − − ⋅           ;@ H+d   <= 67  +   ' E (Z    '( Z $ 0 Z (= g<  F(    ' E$ Z  FB  )+  %  00 /3  1 1 9       F(  &   *  0 0Z *  - 0 3 2( 5 6 7∈ − + = '(  (   1 .W H     (  h ?! - 0 3  3 3  08 (     ; H+d   <= 67  +   ' E (Z    '( Z  $ 0( Z= '( (Z ⊥ H <=!*  (Z    [ & 1 .9 − F(  & www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   01232 + (     &  ( Z $    0 0 8 6 0 26 7+ + − =  <= & (  5B ?! - 0 .  6 .  1 . 0 .  0 . 0 . (  Z− − − −    ;. T +   ' E (Z    (  $ . . 0 Z ( (= =  - / 2( 7 − = g< 9 F(   &+ Z '( . .  0 0        F(+& (Z '( 9 H  ?! - 1 1  . . 9   ⋅       ;/ H+ d   <= 67   +    ' E (Z      Z  $ 0 ( Z (= =  g< /29 F(  & ( '( - 0 2Z 6 7− = H <=&  h ?! - 8 8 . . 0  U U   + +        +d 8 8 . . 0  U U    − − + ⋅         ;0 H+d   <= 67  +   A (Z $!5F:F( Z '( 31 0(Z : = ⋅  r    - . . 2 Z 6 7  (Z− − = ⊥   0 .      ( %  26 >  ?! - - 3 . 04 2( 6 7+ − =    ;7 H+d    " %D/6!5F: Z D B  $    0 26 7− + = [    )+   (Z ' E$':   '(#    & ./      ( %  26 <  ?! - - 0 / 2( 6 7+ − =    ;: T +      ss (Z ( Z $ . .  1 .(  − g+&     )+D B   - 0 . 25 6 7+ − = H <  ?! -  / .   . . Z− − −    K2L MN4O  BC:/ H+d   67  +      ss (Z ( Z $ 2 0    .   Z Z ⊥ =  - 0 0 2Z 6 7+ − = '( 9 F(  &  %  (9 ⊥ H <=& ( h ?! - 3 3  . . (        +d 3 6  . . (   − ⋅     BC:0 H+d   <= 67  +   ' E (Z      Z $ 0 0 ( ( Z= =  H & ( F(& /29  - . . 2Z 6 7− + = H  ?! - 0 . . 0 −  +d . 0 . 0 . 0 − −  BC:7 H+d   <= 67  +   ' E (Z      Z &   (  = ; 6    ( $    1 26 7+ − = =(+  0Z = H <= !*    % > "    %D/0'( =!&   Z   ?! - /22  12  . 0  /2 0 (  Z  +d  02  12  . 0   0 0 (  Z− −  BC:: H+d   67  +      ss (Z ( Z $ 2 0 F(  & (    2/    //  Z 9 Z W Z⊥ ∈ − ∈ H  h ?! - //  BC:; H+d   <= 67  +   A   ss   0(Z ( Z Z (= $ 0 / −  3/( '(&  1 39 − −  =!5F:H <=   Z h ?! - . 3   /2 Z −  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123Y2 BC:< H+d   <= 67  +   A   ss   0   /6(Z(Z ( Z ( Z := =  [   (Z⊥   ./  - 0 2 ( 6 7− + = H <=       (  Z h ?! -  //  . 1  1/  . / (  Z− −  +d . 1   //  . /  1/ (  Z− −  BC:? H+d   <= 67  +      ss   /0  . .  1 .((Z ( Z : ( ∆ = −  g<  F(+&  '( (Z  ` 0   - 0 . 2 (  5 6 7= ∈ + − = H   Z h ?! -  / .   . . Z− − −  +d // // // U   1 1  Z   −     '(F(  IQ  1 /U  . .    − ⋅     BC;@ H+ d   < = 67   +    A (Z  $ 0   .8(ZZ ( := =  '(      )+ - 3 2 6 7+ − = '( - 0 2(Z 6 7− − = H    h ?! - / .  4 .  −  +d 1 /  − ⇒  BC; H+d   <= 67  +   A (Z $ .Z (= '(   )+ ' E$':   - 0 8 2(Z 6 7+ − = H! (Z $ I A  / 0 − H Z h ?! -  3 1Z −  +d /8 4  1 1 Z   ⋅     BC;. H+d   <= 67  +   A (Z $    - 3 2 6 7+ − =  '( - 0 2(Z 6 7− + = H <=!*    %  .8(Z: =  K :t- 0 3( Z= =  BC;/ H+d   <= 67  +   ' E (Z      Z $ 0   6 3Z ( (=  - 0 2Z 6 7− + =  g<  F(      ' E $  Z  FB   '( 60 8  /. /. 9        F(   &   H      Z h K :t- (9 Z9 Z9  ⊥ ← ⊥ ← F( I A 9Z∆  BC;0 H+d   <= 67  +   ' E (Z      ( $ 0 0 Z ( (= =  - 0 2Z 6 7− =  /29 F(  & ( H  h ?! - 3 0 0 0 /  8 8    − −        +d 3 0 0 0 /  8 8   + + ⋅      H 3 Z  Z ← ← =    BC;7 H+d   < = 67   +    ' E (Z      Z  $ !5 F: F( Z    - . 2  - 0 Z 6 7 (Z 6 7− = −  g$ + %V      ( (  %D 31         ( %  01  2(Z (: 6= >  ?! - - 0 / 2( 6 7+ − = '(F(  I  0 2 8+ =  BC;: H+d    "  ! ( %D /0 g+&     )+D B - 0 . 25 6 7+ − = '($ +( = ]!^     Z %  0 (= '( 26 <  ?! - 4 //  3 3 Z−  BC;; H+d   <= 67  +   ' E (Z      Z $ 0 0 ( ( Z= =  /29 F(  &   - . . 2( Z 6 7− + = H  %  Z (>  ?! - . 0 0 0 . .  0 0   + +       '(F(  IQ  .8 =  BC;< H+d   <= 67  +   ' E (Z      ( $ 0 1  .  Z (− =  ?& /  2    . 1  0 9 (  Z   − ∈ − ∈           ( Z %  41(Z: =  ?! - - 6 2Z 6 7− + =  +d - 4 .6 2Z 6 7− + =  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123'2 BC;? H+d    "  %D 41 '(&  / 0( −   - 0 / 2Z 6 7− − = H      Z h ?! - 1 / 2 3   3    2 0 0  Z              '(F(  IQ   0 0 −  BC<@ H+d   <= 67  +      ss (Z ( Z =   +  J A / /  0    −    %  08 '( . 0 0 W   −    F( A  A! +   (Z∆ H Z  ?! -  8 0Z −  +d /6 /3  1 1 Z   − ⋅      X   M Q RNJ S 1     BC< H+d   <= 67  +   + (Z $  )+ - 0 4 2(Z 6 7+ − = '(  - . . 2( 6 7+ − =     % '(  )+JF%  2/  ?! - - U /. 6.  - . /4  - U /. /.  - 0 /( 6 7 Z 6 7 Z 6 7  7 6+ = + = + = = +    ;; H+ d   < = 67   +   + (Z  $ *  / 1  '(    =    )+F( - 0 3 25 6 7− + = ]!^      (  Z %     +$=(%D1 ?! -  0/  ./  8 1(  Z−  +d 8 1 ./  0/(  Z −    ;< H+d   <= 67  +   + (Z $     '(=    )+F( - 4 // 6. 2  - 4 // 1. 2  - 1 . / 2( 6 7 Z 6 7 (Z 6 7− + = − − = − + = H    h ?! -  3 1  8 / − −    ;? T +   + (Z $ /2  . 0 ( '($ /02 ( = H <= *   '( Z h ?! -  . . /  0 ./ . Z− − − +  +d  . . /  0 ./ . Z− − − + −    <@ H+ d   <= 67   +   + (Z  $    )+ - / 2 6 7+ − = & 3U Z 9 (∈ &  1 0 Z− − ∈ '( 0 0 = H  h ?! - . 0 −  +d  / 0 −    < H+ d   < = 67   +   + (Z  $ 1 1          & ( '( Z $    /3 26 7+ + = & 2 3W − D B     Z '(' E$': ( H <=!*    +JF ?! -  4/   // //  / 4(  Z− − − −  +d  / 1   // //   1 /(  Z− − − − − −    <. T +   + (Z $ 282 (Z =  B   ( ( FGF , Ff5!&  9  + + 9( ( (+ = [ &  ./  =   Z '(  A! +$ 9Z $    - . 8 25 6 7− + = H <=*  Z    + (Z  ?! -  . 8/Z −  +d 0/ . . . /Z + +    </ H+ d   < = 67   +   + (Z  $    )+ - 2(Z 6 7− =  '( & / . 9 (∈ &  0 0 .  Z− − ∈ H!*    +%  ( =  ?! - 0 ./   . / . /   / 0 .  0 0 . 0 0 . (  Z− − − − − − − '(  . 0 8= − ⇒ ⋅ ⋅ ⋅    <0 H+d   <= 67  +   + (Z $ A 0/  0   (Z= ?& / 2 . 9        =  ( 24 D B   Z H  % D 1( (=   '( 2(7 >  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123&2 ?! - 13 /.  1 1   ⋅       <7 T +   + (Z +    J 0 0  - 1 1 1 8 .0 6 7− + − = [ D & 46  8U9  FGF ,  =0    '( ( H <=!*    + ?! - ( ) ( )41 68 .1 38   /1 3      1/8 // // // //  (  Z     − −        '(  IQ  - . 0/ 2( 6 7− + =    <: H+d   <= 67  +   + (Z $ A . . $  )+ 0  (Z=  & 3 0  . 9 (   ∈    & /. .  .  Z   ∈          )+ (Z %  .(6 >  ?! - - 8 2(Z 6 7+ − =    <; H+d   <= 67  +   + (Z $!   ( Z FGF , $    F( - 0 1 2  - 0 / 2( 6 7 Z 6 7− + = − + =  '(  . .    / 3 9 Z  (− ∈ − ∈      !    Z (    +h ?! - - 0 . 2  - 0 4 2Z 6 7 ( 6 7+ − = + − =  +d - . 0 /1 2  - . 0 // 2Z 6 7 ( 6 7− + = − + =    K2L MN4O  BC<. H+d   <= 67  +   + (Z $  ( '(  )+ (Z  W+ M I $ D B !    $    / -  4  4 25 6 7+ − =  '( 0 - 0  4 25 6 7+ − =  =  * $ +=F(2/    ! JF ?! - - 0 /  - 4   - /   - 4 .4 2 7 6 ( 7 6 Z 7 6 Z 6 7= + = − = − + − =  BC</ H+d   <= 67  +   + (Z $ A 0/ '( 0  (Z= H<=& / 2  . 9 (   ∈    & 24  Z∈ H ( %  2(6 >  ?! - / /( −  BC<0 H+d   <= 67  +   + (Z $   =   )+F( . 4 26 7+ − = & 2 .( − > "    +%D02H <=       Z  ?! - 0/  2 .  3 1 ( − −  +d 3 1  2 .  0/ ( − −  BC<7 H+ d   < = 67   +   + (Z  $ A / 0 −  '( 0  (Z=  &  1 3 9 (− − ∈ &  1/8  Z− ∈ H ( %  6∈  ?! -  0 6( − −  BC<: H+ d   < = 67   +   + (Z  $    )+ - 0(Z 7 6= −  & 3 3    1/   6 0 (  ( (Z− ∈ − ∈ = H!*    + (Z h ?! - / .  4 1  1 /   / . (  Z− − −  +d /.4  4 1  U//  /1/. (  Z  BC<; H+d   <= 67  +   + (Z $  - 0 / 2( 6 7+ − =   )+ - 0 / 2 6 7+ + = & / .   6 /29 (Z (Z− ∈ = H <=!*    +h ?! -  //  U/  . 4   4 4 (  Z− − − −  +d  //   4 4  . 4  U/ (  Z− − − −  BC<< H+ d   < = 67   +   + (Z  +   0 0  -  0  / 6 6 7− + + =  '( & - 0 . 2  0  0  5 6 7 6 (Z ∈ − + = > = H <=!*    + ?! - / 0  6/  . 3   3 . / 0   3 .  . 3  6/  (  Z  (  Z  − − −  − − −  +d / 6 /U /6    3 1     2 4 1 1 1 1 / 6 /U /6    2 4     3 1 1 1 1 1  (  Z  (  Z      − −         ⋅      − −          www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123Y%2 BC<? H+d   <= 67  +   + (Z $  )+ - 4 ./ 2 6 7+ − = *  / - 6 2( 5 6 7∈ + − = *  0 - 0 . 2Z 5 6 7∈ − + = '( 41(Z: = H       (  Z h ?! - 2 .  26   //8   // (  Z− −  +d  //8  2 6  /2 .   // (  Z− −  BC?@ H+d   <= 67  +   + (Z $     - . / 2( 6 7+ + =    )+ - 1(Z 7 6= + & / 0 9 Z∈ H <=!*    +h ?! - 0 /   3/   84  2 1 (  Z− − −  BC? H+d   <= 67  +   + (Z $  - 0( 7 6= +   )+ -(Z  / 0   02 7 6 9 Z= − ∈ H <=!*    +h ?! - 0U /4 / 1 /4U 44 00 0U           8 8 . . .2 .2 /1 /1  (  Z         − − − − ⋅                  Y   M Q RNJ S        << H+d   <= 67  P5'       5  & 0/9 '( #   J 0 0  - 0 3 3 2 6 7 6 7+ + − − =  W+= A5  ( $=(%D3h ?! - - 0 1 25 6 7+ − =  +d - 0 25 6 7− =    <? H+d   <= 67  P5'       5  & 8 09 '( #   J 0 0  - 0 3 2 6 7 6 7+ − − =   &   ( + + /2( =  ?! - - . 25 6 7− =  +d - . /0 25 6 7+ − =    ?@ H+d   <= 67  P5'       5  & 0 09 '( #   J 0 0  -  /  / /8 6 7+ + − =  0& A%>    ( + + . 9 9(=  ?! - - 3 25 6 7+ − =  +d - 4 /0 25 6 7− − =    ? H+d   <= 67  P5'       5  & / .9 − '( #   J 0 0  - 3 0 /1 2 6 7 6 7+ − + − = ': A      ( + + 6(:∆ = '(  (  F( ( f  ! ( h ?! - - . 25 7 + =  +d - 3 3 1 25 6 7+ + =    ?. H+d   <= 67  +  J 0 0  - 8 6 /8 2 6 7 6 7+ − − + = '( 0 0  3 9   KP5'       5  +!   ,  - b  9 '(#   J    0& + (  !$> " F: f  %b   '(#   J    W+A5  ( $=( ` f  ?! - - 3 25 6 7+ − =  +d - 4 /8 25 6 7+ − = % - / 25 6 7− − =    ?/ FJGHHZIH+d   <= 67  +  J 0 0  - 3 3 8 2 6 7 6 7+ + + + = ': A F(  '(   - 0 . 25 6 7 + − + = H  &   5 #     0& A %>    ( + + (:∆  ! ^F: f h ?! - 2 =  +d 6 /1  = ⋅    ?0 H+d   <= 67  +  J 0 0  - 0 0 /2 2 6 7 6 7+ − + + = $ A  H  &   - / 25 6 7+ + = #        ( + + (∆ @ h ?! - . . = ±    ?7 H+d   <= 67  +  J 0 0  - 0 3 1 2 6 7 6 7+ − + − = KP5'       5 #       9  + + 9∆ ' EA   %  / 2  ?! - - / 25 7 − =  +d - . 25 7 + =  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123Y32   ?: H+d   <= 67  P5'       5  & 0 . '( #    J 0 0/  - /. 6 7+ = '( 0 0 0  - /0 // 2 6 7 6+ − + =  FGF ,    9  + +  F(  & 9  ?! - - . 4 25 6 7− + =    ?; KP5 '        5     &  / 09 −  '( #     J 0 0 /  - 0 . 2 6 7 6+ − − = '( 0 0 0  -  0  . U 6 7− + − =  W+ A5 $=(%D  h ?! - - / 25 6 + =  +d - 3 4 /6 25 6 7− + =    ?< H+ d   < = 67   + 0 0 0 0  -  0  0 3   -  8  0 02 6 7  6 7′− + − = − + − =  g<  F(+&   J$ = KP5'       5     '(#   J     ′  W+ A5  A%> $=(%D   ?! - - 0 25 6 7− + =    ?? H+d   <= 67  +  J 0 0/  -  /  0 1 6 7− + − = ': A / '(  J 0 00  - 0 3 / 2 6 7 6 7+ + + + =  ': A 0   ?   5  + + ':     A   J'(# n R   J$ Bg<   [ FGF , F(      / 0   FB  5       5 %  / 0 /2 [: =  ?! - - 0 1 25 6 7− − =  +d - 0 1 25 6 7− + =   .@@ H+d   <= 67  + 0 0 0 0/ 0  -  /  0 U   -  / /8 6 7  6 7− + − = + + = '(   - 0 3 /1 25 6 7+ − = H& / 0    9   ∈ ∈ + + 9  O   5 F(   I'(  $ +( =A ?! - 3 00     / 3 1 1 9    − −      .@ H+d   <= 67  +  J 0 01  -  / 0 3  6 7   − + − =    KP5L!^  <= !*   ' E (Z %     (  ∈ '(     (  Z 6 6 6∈ >  ?! - 0U 0U 0 0/ 0 0/ 2          2 02 02 1 02 1 02  (  Z         − − ⋅                  .@. H+ d   < = 67   +   J 0 0  -  0  / 1 6 7− + − =  '( - 0 25 6 7+ + =        J  ′ #  5     ( '(#        Z + + (Z F(   ' E% D  Z6 6>  ?! - 0 0  -  / / 6 7′ + + =  +d 0 0  -  / U 6 7′ − + =   .@/ H+d   <= 67  P5'      J   $ A - / 2 5 6 7∈ − − =  '(   #  6      ( #  7    9  + /09 (: :∆ ∆= =  ?! - 0 0 0 0   -  3  . 01   -  .  3 01  6 7  6 7  − + − =  + + + =  +d 0 0 / / 0.21   - 0 0 3  6 7     − + + = ⋅          .@0 H+ d   < = 67   +   J 0 0  - / 6 7+ =  '( & / .  KP5 '      J  ′    n #       (  + +-  04(:∆ =  % L   5  (  ?! - 0 0 / . 1   - 0 0 0  6 7     − + − = ⋅          .@7 T +  J 0 0  -  8  8 12 6 7+ + − = KP5'      5   LY':    & 9 '(#  6    #  7   ( + + 9 F(  &+  (  ?! - - 05 7 6= +  +d - 005 7 6= +  +d - 1 /2 25 6 7− + =  +d - 4 /. /6 25 6 7+ + =  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m          !"   !"  #$%&''&'%%   () *+ $ *,)-. /   0123Y<2  .@: H+d   <= 67  +  J 0 0  -  /  / /2 6 7− + − = '(&  0 19 − −  ?  J A 9 #   J    W+A5  0 1( =      ( h ?! - - 0 0 2( 6 7+ + =  +d - 3 6 . 2( 6 7+ + =   .@; H+d   <= 67  P5'       5  & / 09 '( #   J 0 0  -  0  / 01 6 7− + + =  W+= A5 $=(%D6h ?! - - 0 25 7 − =  +d - . 3 1 25 6 7− + =   .@< H+d   <= 67  P5'       5  & 0/9 '( #   J 0 0  - 0 3 2 6 7 6 7+ − − =     ( + + . 9 9(= −    ?! - - 0 25 6 − =  +d - / 25 7 − =   .@? H+d   < = 67   +  J 0 0  - 3 3 8 2 6 7 6 7+ + + + =  ': A F(   '(    - 0 . 25 6 7 + − + = H   &   5  #     0& A%>    ( + + (∆ @ h ?! - 6 U. 0U  ± = ⋅   . @ FGHHZIH+d  ': > <=kL5 +  J 0 0 3  -  0 1  6 7− + = '(     / 0- 2  - 4 26 7 6 7∆ − = ∆ − = ]!^  <= Ao'(%!Q"   J  ′ %   J  ′   LY': / 0∆ ∆ '( Ao =  JT ?! - 6 3 0 0    1 1 1 [ \   = ⋅      . T +  J ( ) 0 0- /0 3 .8 2 6 7 6 7+ − − + =       J ( )/   LY ':  ; <=kL'(k5n   LY+(':  J ( )  ?! - ( ) ( ) ( ) ( ) ( ) ( )0 0 0 0 0 00 0 3  /6 /6 /6  8 8 .86 7 6 7 6 7− + − = − + − = − + + =   . . T +   J 0 0  - 0 3 0 2 6 7 6 7+ − + + =         J Tu $ A ( )1/9 % Tu# T  & A%> Z[+ + .( =  ?! - 0 0 7 1  7 / /.6 7+ =  +d 0 0 7 1  7 / 3.6 7+ =   . / H+d   <=kL5 +    / - . 25 6 7+ = '( 0 - . 25 6 7− = g<H F(  J  LY':/ Z#  05   &['(T+ + !Z[T' E  [    H% ∆Z[T$> " %D . 0 '(&Z$ +( =  ?! - 0 0 / .   - / 00 .  6 7     + + + =         . 0 T + 0 0/  - 3 6 7+ =  0 0 0  - /0 /6 2 6 7 6+ − + = '(   - 3 25 6 7− − =       J$ A = 0    LY':'(#  /    & A%> Z'([ + +Z[' E$': ?! - 0 0  - 8 8 /2 2 6 7 6 7+ − − + =   . 7 T +!  J ( )0 0/ /  -  / 0 6 7− + = '( ( ) ( ) 0 0 0  -  0 0 3 6 7− + − =          LY':  J /  '(#   J 0   am& 0 09 =  ?! - - 0 2 - 4 8 2 9 6 7 9 6 7  + − =  + − =  +d - 0 2 - 4 0 2 9 6 7 9 6 7  − − = ⋅ − − =  www.MATHVN.com - Toán Học Việt Nam www.DeThiThuDaiHoc.com ww w. M AT HV N. co m

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