ax + by + cxy + dx + ey + f = 0 px + 2y + r = 0 ทที่ 13... · pdf...
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1
1.
AX2 + BY2 + CXY + DX + EY + F = 0 PX + 2Y + R = 0
x y A, B, C, D, E, F, P, Q R A, B C
P, Q
x + 2y = 0 3x y = 12 12x = 3y
3x2 + 2y2 = 10 x2 + xy + y2 = 1
?
1) ... 2)
3) (
) 4)
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2
1 x2 + y2 = 25 ------- x + y = 1 ------- x + y = 1 x x = 1 y ------- x (1 y)2 + y2 = 25 1 2y + y2 + y2 = 25 2 y22y+125 = 0 2 y2 2y 24 = 0 (2y + 6) (y 4) = 0
y = 2
6 , 4 3, 4
y = 3 4 x (3) = 1 x + 4 = 1 x = 4 x = 3
(4, 3) (3, 4)
(3, 4)
(4, 3)
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3
2 x 2y = 8 ------- xy = 24 ------- x x = 2y+8 ------- x (2y + 8) y = 24
y 2y2 + 8 24 = 0 (2y + 12) (y 2) = 0
y = 2, 212
2, 6
y = 2 6 x x 2(2) = 8 x 26(6) = 8 x = 8 + 4 x = 8 12 x = 12 x = 4 (12, 2) (4, 6)
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4
3 2x2 2xy + y2 = 10 ------- 2x y + 2 = 0 -------
x x = 22
2y = 1
2y -------
x y = 2 2
12y
2 2yy1
2y
+
= 10
= 2
+
2
21(1)
2y
2y
2y 010y2y2y 2 =++
= 2 010y2yy1y4y 222 =+
+
= 0102y22y2y 2
=++
= 82y 2 = 0
y = )2(8 y = 4
y = 4 x 2x (4) + 2 = 0 2x (-4) +2 = 0 2x - 2 = 0 2x + 6 = 0
x = 22
= 1 x = 2
6 = -3
(1, 4) (3, 4)
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5
4 24 3
x y y
x = x2 y2
x2 y2 = 24 ------- 2y x = 3 ------- x x = 2y - 3 ------- x y (2y 3)2 y2 = 24 4y2 2(2y) (3) + 9 y2 24 = 0 3y2 12y 15 = 0 (3y 3) (y 5) = 0 y = 5, -1
y = 5 y = 5 2(5) x = 3 10 3 = x x = 10 3 = 7
7 5
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6
5 k y 2x = k y = x2 y 2x = k ------- y = x2 ------- y y = 2x + y ------- = 2x + k = x2 x2 2x k = 0
x x = 2a
4acbb 2
= 2(1)
4(1)(-k)(-2))2( 2
= 2
4k42 + 4k4 = k)4(1+ = k12 +
= 2
)k12(1 +
= l+ 11 k x
x = 1 0
k1+ = 0 1 + k = 0 k = -1
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7
2.
(term) 2
1) ... 2)
3) (
)
6 x2 + y2 = 5 ------- 2x23y2 = 5 ------- 1 x 2 ; 2x2 + 2y2 = 10 -------
2 x y ; 2x2 + 2y2 (2y2 3y2) = 10 5 2x2 + 2y2 2x2 + 3y2 = 5 5y2 = 5 y2 = 1 y = 1
3 y x y = 1 ; x2 + (1)2 = 5 x2 + (-1)2 = 5 x2 + 1 = 5 x2 + 1 = 5 x2 = 4 x2 = 4 x = 2 x = 2 4 (2, 1) (2, 1) (2, 1) (2, 1)
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8
7 2y (x y) = 7 ------- 7y2 4 + xy = 0 ------- ; 2y(x) 2y(y) = 7 2y2 2y2 = 7 2y2 2xy + 7 = 0 ------- ; 7y2 + 1xy 4 = 0 -------
1 xy 2; 14y2 + 2xy 8 = 0 -------
2 xy y + ; 2y2 2xy + 7 +14y2 + 2xy 8 = 0 + 0 16y2 1 = 0 (4y)2 12 = 0 (4y + 1) (4y 1) = 0
y = 41
3 y x
y = 41
;
41
x41
2 = 7
41
x41
2 = 7
41
x21
= 7
+
41
x21
= 7
41
x = 7 2 41
x+ = 7(2)
x = 14 + 41
= 41
14 x = 1441
= 41
14
2 (41
14 ,41
) (41
14 , 41
)
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9
8 22 y1
x1+ =
3613
-------
y1
x1+ =
61
-------
team term
2
y1
x1
+ =
2
61
22
y1
y1
x1
221
+
+
=
361
22 y1
xy2
x1
++ = 361
22 y1
x1+ =
xy2
361 -------
= ()
xy2
361 =
3613
3613
361 =
xy2
3612
= xy2
xy = 6
x = y6
-------
x = y6
y; y1
y6
1+
= 61
-------
y1
6y+ =
61
6y
6y 2 + =
61
y2 + 6 = y y2 + y 6 = 0 (y + 3) (y 2) = 0 y = 2. 3
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10
y = 2. 3 x
21
x1+ =
61
(-3)1
x1+ =
61
x1
= 21
61
x1
= 31
61+
x1
= 62
= 31
x = 63
= 21
x = 3 x = 2 2 (2, 3) (3, 2)
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11
9 a a x2 + y2 = a2 xx y2 = 2a x2 = 4 x2 + y2 = a2 -------
xx y2 = 2a ------- x2 = 4 -------
y x + ; x2 + y2 + x2 y2 = a2 2a -------
2x2 = a2 2a x2 = 4 ; 2(4) = a2 2a a2 2a 8 = 0 (a 4) (a + 2) = 0 a = 4, 2 a a = 4
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12
10 91 77
x xy + y = 91 -------
y xy y = 77 ------- y x xy y
; xy + y y (xy y) = 91 77 xy + y xy + y = 14 2y = 14 y = 7
y = 7 x ; x(7) 7 = 77 x(7) = 77 + 7
x = 7
24
x = 12
12 7
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