( Oy), : , , . ( , , , ). . .. , , . : , , : .
, .
, .
, . . : . : , t . .
, , KL, , ,
, . ..
3.2. .
(.1) , , , R. R > 0 . R ( 0, 0) : ( 0) 2 + ( 0) 2 = R 2. , : 2 + 2 = R 2 |
( 1, 1) (.1), : ( 1 0) ( 0) + ( 1 0) ( 0) = R 2.
y = m x + k 2 + 2 = R 2: k 2 / (1 + m 2 )= R 2.
(.1) , F 1 F 2 , , . (.1): |
, . a > b (.1), a < b Y, a = b ( ). , .
F 1 F 2 = 2 , , . AB = 2 a , CD = 2 b . e = c / a, e < 1 .
( 1, 1) , :
y = m x + k 2 / a 2 + 2 / b 2 = 1:
k 2 = m 2 a 2+ b 2.
(.1) , F 1 F 2 , , . (.1) , . |
F 1 F 2 = 2 , , . AB = 2 a , CD = 2 b . e = c / a, e > 1 . y = (b / a) x .
|
|
( 1, 1) , :
y = m x + k 2 / a 2 2 / b 2 = 1:
k 2 = m 2 a 2 b 2.
(.1) , F, , , .
(.1): y 2 = 2 p x.
.
( 1, 1) , : 1 y = p (x + 1).
y = m x + k y 2 = 2 p x: 2 m k = p.
: + + z + D = 0,
, B C . , B C (.. , ).
0, 0, 0 D 0 :
a = D / A, b = D / B, c = D / C. (a, 0, 0), (0, b, 0) (0, 0, ), .. a, b c.
, ( 0, 0, z 0 ) (, , C): ( 0) + ( 0) + (z z 0) = 0.
+ + z+ D = 0 E+ F+ Gz+ H = 0:
AF BE = BG CF = AG CE = 0.
+ + z+ D = 0 E+ F+ Gz+ H = 0:
E+ F+ G = 0.
( 1, 1, z 1 ) (x 2, y 2, z 2):
( 0, 0, z 0 ) + + z + D = 0:
+ + z+ D = 0 E+ F+ Gz+ H = 0:
, ( 1, 1, z 1) ( 2, 2, z 2):
, ( 0 , 0, z 0) (a, b, ):
+ + z+ D = 0 E+ F+ Gz+ H = 0, ,
.
(a, b, ) (p, q, r) , : aq bp = br cq = ar cp = 0,
: ap + bq + cr = 0,
:
:
R (a, b, ) :
(x a) 2 + (y b) 2 + (z c) 2 = R 2.
|
|
, . , , .
, , . . , (1)
, , (1), . , . - . (2)
(2) .
, : (3)
, .
, : (4)
, , , .
(4) :
, (5)
.
, . (5) .
. .
. . (5) , , . , (5). (1) ,
(∗)
(5), . , (∗) (5), , , (5).
. (5). , ,
, . , (1) .
, , (5), .
, (5) (6)
, , .
, .