e3etaseis Kateu8unshs Bl Me Lyseis
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Transcript of e3etaseis Kateu8unshs Bl Me Lyseis
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1
7 - 2013
:
: :
:
:
: ..
..
1o
. 2 2 2x + y = ( > 0)
1 1A(x , y ) 2
1 1xx + yy = .
10
. ,
;
5 . ,
"" "" ,
: 1, 2, 3, 4 5.
1. H x + y + = 0
(, )
= .
2. 0x x= ( x0 )
xx.
3. 2 2x + y + Ax + By + = 0 2 4 > 0 .
4. ,
= ,
= .
5. ,
= , R .
10 2o
(C) (0, 0), 5=
, , (1, 2) 2 .
) () (C)
1 5
y x2 2
= + .
6 ) , ()
xx, yy, , o
.
7
-
2
) 25
4 .
6
) MN
.
6 3o ( ) A, , (2, 2), (0, 4) (1, 7). ) .
6
) BA B
. 7
) ^
45= , (6, 2). 6
) ^
45= (14, 33),
,
.
6 4o
2
2 2
2t 2t , , t
1 t 1 t
+ + R ()
(2 4)x 2 3y 1 0, + = R .
) (C) (1, 0). 5
) () R . 4
) () ,
(C) () x 3y 1 0 + = .
9 ) ()
(C) () .
7
-
3
2012 2013
. 83. . 41. . 1. , 2. , 3. , 4. , 5. . 2o ) (C)
2 2x y 5+ = ,
(1, 2) :
x 1 y 2 5 + = x 2y 5+ = 2y x 5= +
1 5
y x2 2
= + .
) 2 2
| 0 2 0 5| 5 5 5d(O, ) 5
551 2
+ = = = = =
+.
) () xx y = 0, x = 5, (5, 0), () yy x = 0,
5y
2= ,
5B 0,
2
.
:
55
OA OB 252(OAB)2 2 4
= = = ..
) x = 2, : 2 22 y 5+ = y2 = 1 y = 1, y = 1 ( y < 0).
N(2, 1) ( )MN 2 1, 1 2 (1, 3)
= = .
3o
) 7 2
31 2
+
= =+
,
1
3 = .
( )1y 4 x 03
= 1
y 4 x3
= x + 3y 12 = 0.
-4 -2 2 4 6
-2
-1
1
2
3
4
A
B
()
(C)
M
O
N
-
4
3 2 1 0 1 2 3 4 5 6 7
7
6
5
4
3
2
1
1
2
3
) :
B (1 2,7 2) (3,9) = + + = B (0 2, 4 2) (2,6)
= + + = ,
B
BA B B B B B (3,9) (2,6) 6 54 60
= = = = + = .
) (, ), ,R , B ( 2, 2) = + + ,
BA B ( 2, 2) (3,9) 3 6 9 18 3 9 24 = + + = + + + = + + .
:
3 9 24 60 + + = 3 9 36 + = 12 3 = ().
^
45= , = . :
2 2 2 2(0 ) (4 ) 2 6 + = + 2 2 16 8 40+ + =
() 2 2(12 3) 16 8 40 + + = 2 2144 72 9 16 8 40 + + + =
210 80 120 0 + = 2 8 12 0 + = = 2 = 6 ().
= 2, () = 6 .
= 6, () 6= N .
(6, 2).
) : (1 14,7 33) ( 13,40) = + = .
u// AB
, v (k,m) AB
= u v = + , k, mR .
:
-
5
u// AB
u ( 8, 4) ( 8, 4)
= = , R .
v AB
(k,m) ( 8, 4) 0 = 8k 4m 0 = m 2k=
v (k, 2k)
= .
:
( 13,40) ( 8 , 4 ) (k, 2k) = + 8 k 13
4 2k 40
+ = =
8 k 13
2 k 20
+ = =
8 k 2 k 13 20
k 2 20
+ = +
=
10 7
k 2 20
=
=
7
10
7k 2 20
10
=
=
7
10
93k
5
= =
, 28 14
u ,5 5
= ,
93 186v ,
5 5
= .
4o
)
2 22 22 22
2 2 2 2
2t 2t t 1 2tK 1 0
1 t 1 t 1 t 1 t
= + = + + + + +
4 2 2 4 2
4 2 4 2 4 2
t 2t 1 4t t 2t 11
t 2t 1 t 2t 1 t 2t 1
+ + += + = =
+ + + + + +, = 1,
(C)
(1, 0) R = 1
) y , () .
-2 -1 1 2 3
-1.5
-1.0
-0.5
0.5
1.0
1.5
2.0
K
(x, y)
()
(1)
(2)
) = 2 , :
2 3y 3 0 = 2
3 3 3 3y
22 3 2 3= = = .
-
6
= 1 , :
6x 2 3y 0 + = 2 3
x y6
= 3
x y3
= ,
3 3 1
x3 2 2
= = .
1 3
,2 2
.
:
21 3(2 4) 2 3 1 2 3 1 0
2 2 + = + = ,
()
1 3
A ,2 2
(C) 2 2(x 1) y 1 + = 2 22 2
1 3 1 3 1 31 1
2 2 2 2 4 4
+ = + = + = , A C.
(x, y) , :
KA A 0
= ,
1 3 1 31, x , y 0
2 2 2 2
=
1 1 3 3x y 0
2 2 2 2
+ =
1 1 3 3
x y 02 4 2 4
+ + = 2x 1 2 3y 3 0 + =
2x 2 3y 2 0 + = x 3y 1 0 + = .
) () 1
3
= ,
() 3= y 3x = + .
, d(K,) R= ,
( )2
2
0 3 1
1 3
+ =
+
3 2 = 3 2 = 3 2= .
2: y 3x 3 2= + + 1: y 3x 3 2= + .