Задачи по аналитической геометрии. Микенберг М.А. - 72 стр.

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288x + 225y 400z 1201 = 0
(x5)
2
9
+
(y1)
2
4
(z 2)
2
= 0
2(x z)
2
+ 2(x z)(y z) + 4(y z)
2
7 = 0
4x 12y + 9z 6 = 0
2x + 2y 3z ± 12 = 0
x = 6 +3t y = 2 z = 8+4t x = 6 +9t y = 2 +8t z = 8 + 20t
x2
2
=
y1
1
=
z
1
x4
2
=
y+2
1
=
z
2
3x
2
+ 2xy + 2y
2
+ 3x 4y = 0
x
2
8x y + 15 = 0 9x
2
+ 6xy + y
2
72x 24y + 135 = 0
x
2
4xy + 3y
2
4y = 0
x
2
8y = 0
(7; 5) x + y + 1 = 0
7x
2
+ 4xy + 4y
2
83 = 0
(5; 0) (2; 0) (0; 5) (0; 1)
l = 2
λ = ±5
(1; 0) (0, 5; 2, 5) (1; 0)
7x + 4y + 10 = 0 3x 4y + 18 = 0
2x + 5y = 0 2x + y = 0
7x 2y 13 = 0 x 3 = 0
y + 4 = 0 3x 4 = 0
6x
2
+ 3xy y
2
+ 2x y = 0
x + 2y + 3 = 0 7x 5y + 2 = 0
x + 1 = 0
2x y 8 = 0
17x 4y 4 = 0
49x 49y + 44 = 0
6x 12y + 11 = 0 3x y 7 = 0 2y 5 = 0 3x 3y 2 = 0