Аналитическая геометрия. Шурыгин В.В. - 73 стр.

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M ∈ Φ M Φ
|
−−→
MF
1
| − |
−−→
MF
2
|
= const.
E
2
F
1
F
2
2c F
1
F
2
Φ M
F
1
F
2
2a < 2c
Φ = {M ∈ E
2
:
|
−−→
MF
1
| − |
−−→
MF
2
|
= 2a}.
O
2
O
1
β
S
α
F
2
F
1
A
1
A
2
2a 2c
e =
c
a
> 1
2a
A
1
A
2
Σ
1
Σ
2
2c F
1
F
2
|
−−−→
A
1
A
2
| = |
−−−→
O
1
O
2
|cos α |
−−→
F
1
F
2
| =
|
−−−→
O
1
O
2
|cos β
e =
cos β
cos α
.
+-36 8-)10 M ∈ Φ \ 8- 16|L69 8-)16 M 1-,0)*/1-:- /*)*,09 Φ b 36//;68K
30b6*;-; /72)6* 2L-b7*8b-39*8 /7*L2J}*;2 2/7-b0J†
                          −−→      −−→
                         |M F | − |M F | = const.
                                  1                  2
                                                                  ‚_ڃ
°,-|*/8b- 8-)*1 *b170L-b-M    .7-/1-/80\ 2L-b7*8b-39J}0N 2/7-b0J ‚_ڃ\
,6[b6*8/9 ©Œ¡Ž¬Š‹Š¦= „-),**\ /O-3;27032*; /7*L2J}** -.3*L*7*,0* =
   ϳTxwx™xXWxZ ›œžŸ  ¡‹Š‰ŠžŒ E ª‘ ª”Ž žŠ¤‰Œ F Œ F ¥ žŠ£º
ŒŽ ’Ž»ªœ ‰ŠžŠ‘’Œ ”Š 2c § .Œ¡Ž¬Š‹Š¦  Ɋ‰œ’Œ F Œ F ¢‘”Žžº
                                                         2                 1        2


£ ’Š»Žž”Š Φ ”ŽÐ žŠ¤Ž‰ M ¡‹Š‰ŠžŒ¥ ¬Š‹Àž£ ”Ž‹Œ¤Œ ¢Šº      1        2


žŒ žŠ£Œ¦ Šž ‰ŠžŠ‘Ð ªŠ F Œ F ” Ž‰ŠžŠŠ’œ ¡ŠžŠ£Š’œ
¤Œ‹œ 2a < 2c ¥ žŠ ŽžŸ¥                    1            2



                                  −−→     −−→
                  Φ = {M ∈ E : |M F | − |M F | = 2a}.
                                  2                  1        2
                                                                  ‚_òƒ
   ­ 8-),-/8?J L- .-7-|*,09 ,6 .7-/K
1-/80 :0.*3+-76 -.3*L*79*8/9 .636;*8K
36;0 2a 0 2c = ˆ8,-I*,0* ~80N .636K                                    β
;*83-b
                          c
                  e=        >1                                    O1            F1
,6[b6*8/9 ɝюžŒŒžŽžŠ’ :0.*3K
                          a

+-7=                                                                          A1
   ‡79 :0.*3+-7\9b79J}*M/9 1-,0)*K                                S

/10; /*)*,0*;\.636;*83 2a 36b*, L70,*
                                                                   α

-83*[16 A A b,283*,,*M -+}*M 16/6K                           A2
8*7?,-M .39;-M 1 /O*36; Σ 0 Σ \ 6
          1   2
                                                                                        F2
.636;*83 2c 36b*, L70,* -83*[16 F F
                                  1         2


b,*I,*M -+}*M 16/68*7?,-M .39;-M 1              1 2
                                                                    O2
~80; /O*36;= H-/1-7?12 ‚/;= 30/= Úòƒ
|A A | = |O O | cos α \ 6 |F F | =
 −−−→          −−−→         −−→

|O O | cos β \ 8-
  1   2           1   2               1 2
 −−−→
                                                                  Ç0/= Úò=
  1   2


                 e=
                    cos β
                          .      ‚__ƒ
                          cos α

                                                Ȗ

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