, . .
. .
1. :
- A.
2. - . ,
. . . , , ,
3. ( , ):
31
+ + = 0,
, . . , :
C = 0, ≠0, ≠ 0
= 0, ≠0, ≠0 { By + C = 0}-
= 0, ≠0, ≠ 0 { Ax + C = 0}
= = 0, ≠0
= = 0, ≠0
.
:
1) ,.. :
A1 x + B1 y + C1 z + D1 = 0, A2 x + B2 y + C2 z + D2 = 0; (3.2)
2) M1(x1, y1, z1) M2(x2, y2, z2), , , :
= ; (3.3)
3) M1(x1, y1, z1), , a (m, n, ), . :
. (3.4)
(3.4) .
a .
, (3.4) t:
x = x1 +mt, y = y1 + nt, z = z1 + t. (3.5)
(3.2) x y, :
x = mz + a, y = nz + b. (3.6)
(3.6) , z :
.
(3.2) , - n = [ n 1, n 2], n 1(A1, B1, C1) n 2(A2, B2, C2) - . m, n (3.4) , , ..
; .
x = x1, y = y1; Oz.
|
|
32
x, y, z
Ax + By + Cz +D = 0 (3.1)
, : (3.1), .
n (A, B, C), , . (3.1) A, B, C 0.
(3.1):
1. D = 0, Ax+By+Cz = 0 - .
2. C = 0, Ax+By+D = 0 - Oz.
3. C = D = 0, Ax +By = 0 - Oz.
4. B = C = 0, Ax + D = 0 - Oyz.
: x = 0, y = 0, z = 0.
33-36
. , .
, .
, , .
, , .
: . , , .
, , .
.
, .
, .. .
, , .
37
. , () ( , ).
a - , b - . 2 c - , a, b c ( a > b)
a 2 - b 2 = c 2.
e < 1 ( c < a), .
38
, .
:
a, b ;
- ,
- ;
- ;
- .
, , .
, .
:
a, b ;
- ,
- ;
- ;
- .
, , .
39
. , . , , , - .
|
|
y 2 = 2 px. (*)
p . .
F (*) . ( ) (*)
e = 1.
y 2 = 2 px (p > 0)
40