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
− − =
⋅
− − =
32 trang |
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= * . . − '( - . 0 2 5 6 7∈ + − = H <= ( h
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- . /( − −
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& W Z = - 1 25 6 7+ − =
( h
?!
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/; H+d
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⋅
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r
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?!
- - / 2( 6 7− + = +d - . // 2( 6 7− + =
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( 6 7
− + =
⋅
+ + =
07 T+CO (Z $
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)+
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9
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! S& ( %D 3 H
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-
/88 /88
/
3 3
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U 0
U 0
1 1
9 [
FGF, F( & '( Z H ( Z % 36 >
?!
- /2 / 3 U 3 U2 ( Z
0? H+ d
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- 2ZW 6 7− = H ( Z % 8(Z: = '( 2(7 >
?!
- 2 1 0 1 0 0( Z +d . 0 2 . 0 0( Z
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<= 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
− ⋅
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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
− −
⋅
− −
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BC.< H+d
<= 67 +CO (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 +CO (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/
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67 +& // . U 4 (− − NO
+
+': ( '(# JQ" ( &
A%> Z 9':
'( Z B ( + (= ' Eh
?!
- - 0 1 /2 1 25 6 7+ + ± =
BC/. H+d
<= 67 +' E (Z $ A $+(=%D
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0
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B - . 25 6 7− − = & ( F(+& 5 ': ;+(
H <=!*' Eh
?!
-
U U . . U . /1 .
0 0 0 0 0 0 0 0
( Z
−
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/1 . U . . . U U
0 0 0 0 0 0 0 0
( Z
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'
Z % 9 Z⊥
?!
-
// /. /. U /4 0 0/
- 0 2
1 1 1 1 1
( Z 6 7
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& / 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
⋅
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< = 67 + 0 . 1 0 68 ( H & - . 2Z 5 6 7∈ − + = &
' E 9
$! 9
9 !& ( Z ++>
" 9
! ^F:f h
?!
- 4/2Z +d 04 03Z − −
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A!
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& 0 0 − ∈ Z ]!^ <=!*' Eh
?!
- / 1 ./ / . 1/ ( Z− − +d ./ / 1 1/ / . ( Z− −
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- 02 +d
0 6
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Z ` 0 9 9Z= H <= ( Z % - 0 1 29 6 7− − =
?!
- / . / / // . / ( Z− − − − '(F(
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BC0@ H+d
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& 2 0 Z∈ ++ 9∆ A H <=!*' Eh
?!
- / 1 1 . . . ./ ( Z− − − − '(F(
I': . 2 8+ =
BC0
H+d
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g< 9 F(&D B ( ++ 0 9 (= F( ' E$
( B 9Z H ( %
1 /
0 0
− ⋅
?!
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BC0. H+d
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& 1/ H <=!*CO (Z
?!
-
. . 3 3 4/ 82
. . 0 0 / 1 28
( Z
( Z
−
'(F(
I':
,
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1 1
⋅
BC0/ H+d
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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 '( *
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CO (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
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( '( F(& B ++
/
3
= - / 29 6 7− + = H <=!
*JF' E% 296 >
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-
/ 0 4 8 . /3
1 1 1 1 1 1
(
−
'(F(
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BC0< H+d
<= 67 +' E (Z $ / 09 F( & (
r
5Qj S Z9∆ F( - 1 / 25 6 7− + = H ( % 26 >
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-
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J
0 0 - 0 / / 6 7− + + = ?)+ - 0 / 2 5 6 7⊥ − − = H ( % 6 6<
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U 0
1 1
(
−
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0 1 1
/ /
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± − ⋅
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- / / 2/( Z− +d
. / 6 /
1 1 1 1
( Z
− − ⋅
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T+CO (Z $
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- / 2
1 1
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BC7. T+ C O (Z $ . - 0 U 2 3 1 / 0 (Z: 6 7 9 ( Z= + − = − ∈ ∈ H
<=* % * $+(=Ah
?!
- 0 0 . 8 0 ± − ∓
BC7/ T+CO (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
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S
1
1
7@ H+d
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=!* /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
?!
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7/ H+d
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I+ Z '( 0 - 1 . 26 7∆ + − = F(
A!$
(
]!^ <=!*JF%(
?!
- / 0 1 3 02 ( − −
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70 H+ d
< = 67 + (∆ $ + Qj S * ( $
F(
/ 26 7+ + = < Z F( & LM & ( H <= !
* ! (∆ % <=& . 3Z '( /2 − F( I A (∆ &
$ <= 5B'( = 0 8 26 7− − =
?!
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77 H+d
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A 3 ( = '(
0/ /6
1 1
[
F( & ( L H <=!
*%( (Z % - . 2( 5 6 7∈ + − = n ( 6 6 ∈
?!
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7: FGHVIH+d
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3
.
.
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?!
-
4 / 4 /
0 0 0 0
− − ⋅
7< H+ d
67 + % ( (Z $ * / 1( < F(
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A! +(
F( - /5 7 6= − H <= Z
?!
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7? H+ d
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0 / 26 7+ + = ?& 9 D B Z ++ 9 =
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- ( )/ /.0 /0 6 4
0 0
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( 6 7 ( 6 7 Z 6 7 Z 6 7
− − = − + = − − = − − =
⋅
+ − = + − = + − = + + =
:
H+d
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=!*%( (Z % .0Z: = '( 27 >
?!
- 18 /6 . 0 / 3 ( Z− − −
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67 +%( (Z $ A / . − '( < A (Z∆ F(
&
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⋅
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F(
5Qj S* J 0 0 - . . /2 6 7− + − =
?!
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012342
:/ H+d
67 +%( (Z $ (Z∆ ' E Z K ' E
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1 1 1 1
[
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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( . .
?!
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=
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!$Z FGF, F( 0 / 26 7− − = '( 7/ 26 = ]!
^ <=!*JF%( (Z
?!
- / 0 1 . / / ( Z − −
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#$%&''&'%%
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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( &
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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 −
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!" !"
#$%&''&'%%
() *+ $*,)-. /
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− + =
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!" !"
#$%&''&'%%
() *+ $*,)-. /
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 >
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!" !"
#$%&''&'%%
() *+ $*,)-. /
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
− −
⋅
− −
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!" !"
#$%&''&'%%
() *+ $*,)-. /
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 + =
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!" !"
#$%&''&'%%
() *+ $*,)-. /
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+ + =
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!" !"
#$%&''&'%%
() *+ $*,)-. /
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
− − =
⋅
− − =
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