Аналитическая геометрия. Шурыгин В.В. - 76 стр.

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O
F
1
F
2
M
r
1
r
2
d
1
d
2
D
1
D
2
M(x; y)
y
2
=
b
2
a
2
x
2
− b
2
y
2
M
|
−−→
MF
1
| =
p
(x + c)
2
+ y
2
|
−−→
MF
2
| =
p
(x − c)
2
+ y
2
x 6 −a
|
−−→
MF
1
| = −a −
c
a
x, |
−−→
MF
2
| = a −
c
a
x,
x > a
|
−−→
MF
1
| = a +
c
a
x, |
−−→
MF
2
| = −a +
c
a
x,
|
−−→
MF
1
| − |
−−→
MF
2
| = ±2a M ∈ Φ
Φ
1
Φ
2
e
1
= e
2
= e
a b
a
2
= λa
1
c
2
= a
2
e = λa
1
e = λc
1
                       D2                               D1

                                               d2               d1
                                                                          M
                                  r2
                                                                     r1
                     F2           O                             F1




                               Ç0/= Úã=
€*832L,- 2+*L08?/9\ )8-ã b/9169 8-)16 M (x; y) \ 1--3L0,68 1-8-3-M 2L-
                                                                     _ò
                                                                        K
b7*8b-39J8 236b,*,0J ‚ •ƒ\.30,6L7*|08 36//;6830b6*;-M :0.*3+-7* ‚ ƒ=
‡*M/8b08*7?,-\ 236b,*,0* ‚㕃 ~1b0b67*,8,- /7*L2J}*;2† y = x − b =                            b2 2
H-L/86b799 ~8- b36|*,0* L79 y b O-3;27 L79 36//8-9,09 -8 M L- O-K
                                                                                      2                  2
                                                                                              a2
                                  2
12/-b |−M−F→| = p(x + c) + y 0 |−M−F→| = p(x − c) + y \ .-/7* .30b*L*,09
.-L-+,N )7*,-b .-72)0;\ )8- L79 8-)*1 :0.*3+-7 / 6+/ 0//-M x 6 −a
                          2   2                                       2       2
          1                                2


                   −−→            c      −−→
                  |M F | = −a − x, |M F | = a − x,
                                                    c                ‚ã]ƒ
6 L79 8-)*1 :0.*3+-7 / 6+/ 0//-Ma x > a
                      1                                     2
                                                    a

                   −−→          c       −−→
                  |M F | = a + x, |M F | = −a + x,
                      1
                                                    c
                                                    2
                                                                     ‚ãƃ
                                a                   a
                )
-812L6 /7*L2*8\ 8- |M F | − |M F | = ±2a \ 8- */8? M ∈ Φ =
                    − −→     −− →

   „610; -+36[-;\ b/9169 :0.*3+-76 ;-|*8 ã+8? [6L6,6 b ,*1-8-3-M .39K
                          1        2


;-2:-7?,-M /0/8*;* 1--3L0,68 236b,*,0*; ‚ •ƒ= “8- 236b,*,0* ,6[b6*8/9
‰ŠŒ¤Ž‰Œ’= ­0/8*;6 1--3L0,68\ b 1-8-3-M ~770./ 0;**8 236b,*,0* ‚㕃\
,6[b6*8/9 ‰ŠŒ¤Ž‰Š¦ L79 ~8-M :0.*3+-7=
   ð͵xñÍXW´Z
   •= —[ 236b,*,09 ‚㕃 /7*L2*8\ )8- ª”Ž ©Œ¡Ž¬Š‹‘ Φ Œ Φ ¥ Œ’ŽÀ«ŒŽ ŠªŒº
‰Š”‘¦ ɝюžŒŒžŽž e = e = e ¥ ¡ŠªŠ¬‘= ‡*M/8b08*7?,-\ b ~8-;         1       2


/72)6* .636;*83 a 0 b 0[ 16,-,0)*/10N 236b,*,0M ~80N ~770./-b -16[K
                              1        2


b6J8/9 .3-.-3 0-,67?,;0† */70 a = λa \ 8- c = a e = λa e = λc \ 6\
                                           2            1            2        2           1          1
                                     ÈÁ

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