Аналитическая геометрия. Шурыгин В.В. - 63 стр.

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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}.
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
.
O
2
O
1
α
S
β
A
2
A
1
F
1
F
2
F
1
= F
2
= O
a
O a
O
Φ M ∈ Φ r
1
= |
−−→
MF
1
|
r
2
= |
−−→
MF
2
| M
°,-|*/8b- 8-)*1 *b170L-b-M   .7-/1-/80\ 2L-b7*8b-39J}0N 2/7-b0J ‚Ú`ƒ\
,6[b6*8/9 ˋŒ¡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 § ߋ‹Œ¡Š’  Ɋ‰œ’Œ F Œ F ¢‘”Žž£
                                                              2               1       2


’Š»Žž”Š Φ ”ŽÐ žŠ¤Ž‰ M ¡‹Š‰ŠžŒ¥ œ’’ žŠ£Œ¦ Šž ‰ŠžŠ‘Ð       1           2

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
                                                                  ‚ò^ƒ
                                                                  2
 ­ 8-),-/8?J L- .-7-|*,09 ,6 .7-/1-/80 ~770./ -.3*L*79*8/9 Lb2;9 .6K
36;*836;0 2a 0 2c = ˆ8,-I*,0* ~80N .636;*83-b
                                                        c
                                                e=        <1
                                                        a
,6[b6*8/9 ɝюžŒŒžŽžŠ’ ~770./6=
   ‡79 ~770./6\ 9b79J}*:-/9 1-,0)*K                S

/10; /*)*,0*;\.636;*83 2a 36b*, L70K
,* -83*[16 A A b,*I,*M -+}*M 16/6K                    α

8*7?,-M .39;-M 1 /O*36; Σ 0 Σ \ 6
                  1   2


.636;*83 2c 36b*, L70,* -83*[16 F F     1
                                                 O
                                                    2       A
                                                                      1
                                                                                      1

b,283*,,*M -+}*M 16/68*7?,-M .39;-M                 1 2


1 ~80; /O*36;= H-/1-7?12 |−A−−A→| =                       F                       1


|O O | cos α \ 6 |F F | = |O O | cos β \ 8-
                                            1   2
 −−−→             −−→       −−−→
           ^
                                                   β
‚/;= 30/= Ú ƒ
  1   2                   1 2   1   2

                                            F                     2

                 e=
                     cos β
                           .          ‚ò•ƒ                                                       A2
   { /72)6*\1-:L6 O-12/
                     cos α
                               ~770./6 ‚ò^ƒ
/-b.6L6J8† F = F = O \ ~770./ .3*LK
                                                    O                     2


/86b79*8 /-+-M ;,-|*/8b- b/*N 8-)*1\
                  1        2


,6N-L9}0N/9 ,6 36//8-9,00 a -8 8-)K
10 O \ 8- */8? Š‰œ»ŠžŸ 36L02/6 a               0/   Ú ^=
                  )
/ *,83-; b 8- 1* O = “1/ *,830/08*8              Ç   =
-132|,-/80 36b*, ,27J=
   H2/8? ~770./ Φ ,* 9b79*8/9 -132|,-/8?J 0 M ∈ Φ = >0/76 r                                      −−→
0 r = |−M−F→| ,6[b6J8/9 Ɋ‰‹Ÿ‘’Œ ªŒœ’Œ 8-)10 M =                                   1   = |M F1 |
  2           2
                                         Á–

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