BÀI TẬP PHƯƠNG PHÁP TỌA ĐỘ TRONG MẶT PHẲNG doc

BÀI TẬP PHƯƠNG PHÁP TỌA ĐỘ TRONG MẶT PHẲNG
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=
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PT c¹nh BC ®i qua B(2 ; -1) vµ nhËn VTCP
( )
$
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cña (d
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2
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a :/$
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2
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 : &  ;
 . ;/:0
: ( "' &  :
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=−−++−⇔=−+−
ayxyxayyxx
D+.08
1&$"(
$$
=−−
ayx
f+,+ 

(!,!$"%&1
v+ (!,!$"%&1 56(!,!$"%&1
Y )*+,r.(/$08,%(1
Y)LB56 &/(01
2@2)S+S).
$
/
$
0T
( )
1 1
4 ( 4) 4 0x x y y- - + - =
D)S+S*+, &/,08
( )
1 1
4 ( 4) 4 0x ya- - + - =
vK,.
"
/
"
0W,
( )
2 2
4 ( 4) 4 0x y a- - + - =
f+,56(!,!$"%&1
Bài 10 : 7J)9K, R.0
$
""
=+
yx

12)2nv4,L
8 %l)w")L6_x))LL@cC,))S+S7J).0G,
),,))S+S>?V&

1
Giải :
Y RO.&/&076>2@AZ%$1
M)^GuEE56,))S+S.562)S)L01
• kS+
POPBPA
o
⇒=⇒=
"V&
e
+ R.
$
0O>2@AZ%"1
• kS+
POPBPA
o
⇒=⇒=
:
"
$"&
e
+ R.
"
0O>2@AZ%
:
"

1
Y %W,`8+B+>6)2Q R.
$
076@P)L+7J) R
.
"
01
• Y %Q.
$
0
"" <<−⇔ m
1
• Y %@P)L+7J)
.
"
0
:
"
−<⇔ m

1
:
"
>m
f+,2)2nB4,56
1"
:
"
:
"

"
<<−<<−
mvam 
Bài : 7J)9K,>, 
T
$
"#!:%&T
"
#"!(%&76T
:
"!!"%&1
D)S RO+T
$
76)Swl )7J)T
"
T
:
1
Giải :
MK)N56O76@A)9+Z56>2@A4, R1
D
$
I d
∈
8K,4,NTN%./:!"01
Y R.N0)Sw7J)T
"
76T
:
@)763@)

T.N/T
"
0%T.N/T
:
01.h0
,
( )
( ) ( )
" : " ( " : " "
h
; ;
t t t t
+ − − − − −
⇔ =

:
: " ( ;
$
t
t t
t
=

⇔ − = − ⇔

=

I DJ)%:,N%.:I:076
'
;

R
=
/
I DJ)%$,N%.$/$076
$
;
R
=
1
D,) RW,`8+B+>6)2/4,w56
( ) ( ) ( ) ( )
" " " "
(d $
: : 6 I$ $
; ;
x y v y− + + = + − =
Bài 11: 7J)9K, .I$0
"
#.#:0
"
%d76 T
!#$%&185X)L-768T5X)LkG,iK,56+)L4,-k1K,
4,2)L-76k
Giải :
D
N d
∈
8K,4,kTk%./#$01
D-76ki)=7J),+*+,8-%.I/II$01
D

M C
∈
8
( ) ( ) ( )
" "
$ $ : d1 ht t
− − + − − + =
,
( )
"
h " & $ "1
⇔ − − = ⇔ = − =
t t t hay t
I DJ)%I$,-%.$/&076k%.I$/&01
DJ)%",-%.I"/I:076k%."/:01
Bi 12 : 7J)9K,,) T
$
#!"%&76
T
"
"!#:%&18T
$
5X)L-768T
"
5X)LkG,
" &OM ON
+ =
uuuur uuur r
1K,4,
)L-76k1

Gii :
D
$
M d

8K,4,-T-%.,/"!,01
D
"
N d
84,kTk%.>/">#:01
,
( )
" &
" &
" &
" " " : &
( H
a b
a b
OM ON
a b
a b
+ =

+ =


+ =

+ + =

=



uuuur uuur r
H (
1
: :
a b = =
D
H " ( $
/ 6 k% I / 1
: : : :
M v

=
ữ ữ

Bi 13: 7J)9K,,)27J)
; . $/ $0AB C
=

#"!:%&76KO4,,)2+ #!"%&1a`K,
23761
Gii :
MK)N./056+)L4,76M.
M
/
M
056KO4,1

"
:
CG CI
=
8
" $ " $
/ 1
: :
G G
x y
x y

= =
f+,K,)LNW,`9
" : &
.;/ $0
" $ " $
" &
: :
x y
I
x y
+ =




+ =

1
;
" "
AB
IA IB
= = =
8K,2)L56,))9@2,+4,9
" "
" : & (
; $
. ;0 . $0
( "
x y x
x y y

+ = =




+ + = =




V
:
1
"

x
y
=



=


1K,4,2)L56
$ :
(/ V/ 1
" "


ữ ữ

Bi 14 : Trong mặt phẳng Oxy cho tam giác ABC biết A(2; - 3), B(3; - 2), có diện tích bằng
:
"
và trọng tâm
thuộc đờng thẳng

: 3x y 8 = 0. Tìm tọa độ đỉnh C
Gii
Ta có: AB =
"
, trung điểm M (
; ;
/

" "

), pt (AB): x y 5 = 0. S
ABC
=
$
"
d(C, AB).AB =
:
"

d(C, AB)=
:
"
Gọi G(t;3t-8) là trọng tâm tam giác ABC thì d(G, AB)=
$
"

d(G, AB)=
.: H0 ;
"
t t
=
$
"

t = 1 hoặc t = 2

G(1; - 5) hoặc G(2; - 2)
Mà

:CM GM=
uuuur uuuur

C = (-2; -10) hoặc C = (1; -1)
Bài 15 :  R.0x
2
+ y
2
= 1;76x
2
+ y
2
– 2(m + 1)x + 4my
– 5 = 0 (1)=)?.$0564, R7J)K)1MK)2 
R=56.

01L.

0)Sw7J).01
Giải:
.0O.&/&0>2@AZ%$.

0OI.#$/I"0>2@A
" "
b . $0 ( ;R m m= + + +
N
" "
. $0 (m m= + +
,NyZm
 D.076.


03)S+1%%[Zm!Z%N.7Zm[Z0
M)^),%I$/%:];
Bài 16 :K,.0,)2KOM
$$
$/
:
 
 ÷
 
 
+v4,
−
:#H%&76 
(#!d%&1s2nK,234,,)21
Giải
,+ 8.,/d!(,0.>/d!(>0
M.$/
$$
0
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