Аналитическая геометрия. Шурыгин В.В. - 82 стр.

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u = {l; m}
u = {l; m}
D(u)
v = {l
0
; m
0
} =
∓
m
b
2
;
l
a
2
.
v
D(v) v
l
0
m
0
l m
l
0
x
a
2
±
m
0
y
b
2
= 0 ⇐⇒ ∓
mx
a
2
b
2
±
ly
a
2
b
2
= 0 ⇐⇒ −mx + ly = 0.
D(v)
u = {l; m}
D(u) D(v)
Φ ( ) u = {l; m}
v = {l
0
; m
0
} Φ
u = {l; m} v = {l
0
; m
0
}
Φ
l
0
m
0
= ∓
ma
2
lb
2
⇐⇒
ll
0
a
2
±
mm
0
b
2
= 0.
Φ
Φ
u = {l; m} v = {l
0
; m
0
}
Φ
Φ
u = {l; m} v = {l
0
; m
0
}
ll
0
+ mm
0
= 0,
ll
0
a
2
±
mm
0
b
2
= 0.
ll
0
= −mm
0
1
b
2
∓
1
a
2
= 0.
¡”‹ŽŒ£ u = {l; m} ¥ Œ‹Œ¥ ¡ŠžŠ¥ ªŒ’ŽžŠ’¥ Š¡£»Ž‘’ ŽŒ’¡º
žŠžŒ¤Ž‰Š’œ ¡”‹ŽŒÀ u = {l; m} §
   —[ 236b,*,09 ‚a]ƒ /7*L2*8\ )8- L06;*83 D(u) 0;**8 ,6.36b79J}0M b*1K
8-3
                                                                    ‚aƃ
                                             
                                     0   m l 0
                       v = {l ; m } = ∓ ;       .
Ó*:1- .3-b*308?\ )8- ,6.36b7*,0*\ [6L6b6*;-*
                                                                 2   2
                                         b a
                                                b*18-3-; v \ ,* 9b79*8/9
6/0;.8-80)*/10;= €6ML*; L06;*83 D(v) \ /-.39|*,,M ,6.36b7*,0J v =
H-L/86b799 b 236b,*,0* ‚a]ƒ l 0 m b;*/8- l 0 m \ .-72)6*;
                                     0           0

    l 0 x m0 y                       mx     ly
         ± 2 =0             ⇐⇒   ∓        ±      =0                      ⇐⇒          −mx + ly = 0.
„610;  -+36[-;\ ,6.36b79J}0; b*18-3-; L06;*836 D(v) 9b79*8/9 .*3b-K
    a2     b                         a2 b2 a2 b2

,6)67?,- [6L6,,M ,6.36b79J}0M b*18-3 N-3L u = {l; m} =
   ϳTxwx™xXWxZöŒ’Žž‘ D(u) Œ D(v) ¢‘”Àž£ Š¡£»Ž‘’Œ ªŒº
’Žž’Œ ‰Œ”Š¦ Φ ¥ ŒÐ ¡”‹ŽŒ£ ( Œ ¡”‹£À«ŒŽ ”Ž‰žŠ‘) u = {l; m}
Œ v = {l ; m } ¢‘”Àž£ Š¡£»Ž‘’Œ ŠžŠŒžŽ‹ŸŠ ‰Œ”Š¦ Φ §
        0   0
   —[ /--8,-I*,0M ‚aƃ /7*L2*8\ )8- ,6.36b7*,09 u = {l; m} 0 v = {l ; m }                        0   0
/-.39|*, -8,-/08*7?,- 130b-M Φ 8-:L6 0 8-7?1- 8-:L6\ 1-:L6
                   l0
                       =∓
                          ma     2
                                  ⇐⇒
                                           ll
                                              ±
                                                mm
                                                       = 0.
                                                                 0
                                                                        ‚aڃ     0


{/9169 .39;69 ,*6/0;.8-80
                   m    0  lb
                             )*/1-:- ,6.36b7*,09\
                                 2         a     b
                                                     .3-N-L9}69 )*3*[ *,83
                                                                 2           2


130b-M Φ \ 9b79*8/9 L06;*83-;\ /-.39|*,,; ,*1-8-3-;2 ,6.36b7*,0J
‚~8- ,6.36b7*,0* ;-|,- ,6M80 0[ 236b,*,09 ‚aڃƒ=
   ϳTxwx™xXWxZ .‹”‘’Œ ¡”‹ŽŒ£’Œ ‰Œ”Š¦ Φ ¢‘”Žž£ ¡ º
¡”‹ŽŒ¦ u = {l; m} Œ v = {l ; m ª} ¥ ‰ŠžŠ‘Ž    ŠªŠ”Ž’ŽŠ Š¡£»Ž‘
ŠžŠŒžŽ‹ŸŠ Φ Œ ŠžŠ©Š‹Ÿ‘ Š Š ªœ©Š’œ§
                                         0       0


   ‡79 ,6N-|L*,09 :76b,N ,6.36b7*,0M 130b-M Φ ,6L- ,6M80 .632 ,6K
.36b7*,0M u = {l; m} 0 v = {l ; m } \ 2L-b7*8b-39J}0N /0/8*;* 236b,*,0M
                                     0       0


                            0
                     ll + mm = 0,0      ll
                                            ±
                                              mm
                                                   = 0.
                                                             0
                                                                        ‚aòƒ
                                                                         0


—[ .*3b-:- 236b,*,09 ‚aòƒ .-72)6*; lla= −mm    b
                                                   =  H-L/86b799 ~8- /--8,-K
                                                             2       2


I*,0* b- b8-3-* 236b,*,0* ‚aòƒ\ .-72)6*;
                                                         0               0



                                1
                                  ∓
                                      1
                                        = 0.
                                         2           2
                                                                        ‚a_ƒ
                                b    a
                                     Ôï

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