Аналитическая геометрия. Шурыгин В.В. - 64 стр.

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MP
2
A
2
MP
2
C
2
Φ
|
−−→
MP
2
| = |
−−−→
MC
2
|cos β |
−−→
MP
2
| = |
−−−→
MA
2
|cos α
|
−−→
MF
2
|
|
−−−→
MC
2
|
=
|
−−−→
MA
2
|
|
−−−→
MC
2
|
=
cos β
cos α
= e.
MP
1
A
1
MP
1
C
1
|
−−→
MF
1
|
|
−−−→
MC
1
|
=
|
−−−→
MA
1
|
|
−−−→
MC
1
|
= e.
D
2
D
1
Φ
M d
1
=
|
−−−→
MC
1
| d
2
= |
−−−→
MC
2
|
M
M
r
1
d
1
=
r
2
d
2
= e.
Φ
F
1
F
2
F
1
F
2
F
1
F
2
E
2
F
1
(−c ; 0) F
2
(c ; 0) M(x; y)
p
(x + c)
2
+ y
2
+
p
(x − c)
2
+ y
2
= 2a.
   —[ 36//;-83*,09 .39;-2:-7?,N 83*2:-7?,01-b M P A 0 M P C L79
~770./6 Φ \ 9b79J}*:-/9 1-,0)*/10; /*)*,0*; ‚30/= Æ`ƒ\ .-72)6*;\ )8-       2   2             2   2


|M P | = |M C | cos β \ |M P | = |M A | cos α = ˆ8/JL6 /7*L2*8\ 8-
 −−→
    2
           −−−→
                 2
                         −−→
                             2
                                  −−−→
                                             2
                                                                   )
                                                                             ‚ò]ƒ
                           −−→       −−−→
                          |M F | 2  |M A | cos β 2
                           −−−→ = −−−→ = cos α = e.
                          |M C |    |M C |
Ç6//;6830b69    .39;-2:-7?,* 83*2:-7?,010 M P A 0 M P C \ .30L*; 1
                                 2               2


6,67-:0),-;2 /--8,-I*,0J                                       1       1           1   1



                                                                             ‚òƃ
                               −−→       −−−→
                              |M F | 1  |M A |         1
                               −−−→ = −−−→ = e.
H39;* D 0 D ,6[b6J8/9|MªCŒŽ‰žŒ’Œ
                                    |1  |M C |
                                                 ~770./6 Φ = Ç6//8-9,09 -8 8-)K
                                                       1


10 M ~770./6 L- *:- L03*1830/ -+-[,6)6J8 /7*L2J}0; -+36[-;† d =
             2       1


|M C | \ d = |M C | =
                                                                                                     1
 −−−→         −−−→
   —[ .-72)*,,N /--8,-I*,0M ‚ò]ƒ 0 ‚òƃ b8*16*8 /7*L2J}** /b-M/8b-
     1   2               2


~770./6=
    ¿žŠÄŽŒŽ    Ɋ‰‹ŸŠ©Š ªŒœ žŠ¤‰Œ M ˋŒ¡ ‰ žŠ£ŒÀ Šž
ފ¦ žŠ¤‰Œ ªŠ ŠŠž”Žžž”œÀ«Ž¦ ªŒŽ‰žŒ‘ Ž ¢”ŒŒž Šž ”‘¬Š žŠ¤º
‰Œ M Œ ”Š ɝюžŒŒžŽžœ ˋŒ¡†
                                  r  1
                                      =
                                        r
                                           = e.
                                                 2                           ‚òڃ
   ð͵xñÍXWxZ {I*.30b*L*,,*     d  1  d
                                      36//2|L*,09 -8,-/98/9 1 ~770./2\ 9b79K
                                                 2


J}*;2/9 1-,0)*/10; /*)*,0*;= €0|* +2L*8 216[6,-\ 161 ,6N-L98/9 L03*1K
830/ .3-0[b-7?,-:- ~770./6\ -.3*L*7*,,-:- 2/7-b0*; ‚ò^ƒ=
   ,ÍXuXWñx¶yux STÍtXxXWx -™™W³¶ÍZ
   Ç6//;-830; ~770./ Φ \)-.3*L*7*,,M 161 ;,-|*/8b- 8-)*1 ‚ò^ƒ= —[ ~8-K
:- -.3*L*7*,09 /7*L2*8\ 8- .39;69 F F 0 .*3.*,L012793 1 F F \ L*79K
}0M -83*[-1 F F .-.-76;\ 9b79J8/9 -/9;0 /0;;*8300 ~770./6= {+*3*;
                                                     1 2                                   1 2


.39;-2:-7?,2J /0/8*;2 1--3L0,68 ,6 .7-/1-/80 E \ b 1-8-3-M ~80 .39;*
                     1 2


9b79J8/9\ /--8b*8/8b*,,-\ -/9;0 6+/ 0// 0 -3L0,68 ‚/;= 30/= ڕƒ= { ~8-M
                                                                   2


/0/8*;* 1--3L0,68 O-12/ ~770./6 0 .3-0[b-7?,69 8-)16 .7-/1-/80 0;*K
J8\ /--8b*8/8b*,,-\ 1--3L0,68 F (−c ; 0) \ F (c ; 0) \ M (x; y) \ 6 /--8,-I*,0*
‚ò^ƒ .30,0;6*8 b0L                       1                 2


                   p
                                 2   2
                                        p
                      (x + c) + y + (x − c) + y = 2a.      2   2             ‚òòƒ
                                        Á¸

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