Аналитическая геометрия. Шурыгин В.В. - 75 стр.

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|
−−→
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.
x
2
a
2
−
y
2
b
2
= 1,
b
2
= c
2
− a
2
6,67-:0),-;2 /--8,-I*,0J
                                                                            ‚_aƒ
                                 −−→     −−−→
                                |M F1 | |M A1 |
                                 −−−→ = −−−→ = e.
                                |M C1 | |M C1 |
H39;* D 0 D ,6[b6J8/9 ªŒŽ‰žŒ’Œ :0.*3+-7 Φ = ˆ+-[,6)0; 36/K
/8-9,09 -8 8-)10 M :0.*3+-7 L- L03*1830/ )*3*[ d = |−M−−C→| \ d =
              2       1

 −−−→ —                  _ã _
|M C | = [ /--8,-I*,0M ‚ ƒ 0 ‚ aƒ b8*16*8 /7*L2J}** /b-M/8b- :0.*3+-K
                                                           1          1     2


7= 2


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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 ©Œ¡Ž¬Š‹‘†
                              r
                                =
                                   r    1
                                      = e.
                                            2                              ‚_`ƒ
                              d    d
   ð͵xñÍXWxZ {I*.30b*L*,,* 36//2|L*,09 -8,-/98/9 1 :0.*3+-7*\ 9bK
                                        1   2


79J}*M/9 1-,0)*/10; /*)*,0*;= €0|* +2L*8 216[6,-\ 161 ,6N-L98/9 L0K
3*1830/ .3-0[b-7?,-M :0.*3+-7\ -.3*L*7*,,-M 2/7-b0*; ‚_òƒ=
   ,ÍXuXWñx¶yux STÍtXxXWx VW³xTvu™UZ
   Ç6//;-830; :0.*3+-72 Φ)\ -.3*L*7*,,2J 161 ;,-|*/8b- 8-)*1 ‚_òƒ= —[
~8-:- -.3*L*7*,09 /7*L2*8\ 8- .39;69 F F 0 .*3.*,L012793 1 F F \ L*K
79}0M -83*[-1 F F .-.-76;\ 9b79J8/9 -/9;0 /0;;*8300 :0.*3+-7= {K
                                                1 2                   1 2


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


.39;* 9b79J8/9\ /--8b*8/8b*,,-\ -/9;0 6+/ 0// 0 -3L0,68 ‚/;= 30/= Úòƒ= {
                                                               2


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


                 p
                                2
                                 p
                                    2             2
                   (x + c) + y − (x − c) + y = ±2a.   2                    ‚ã^ƒ
   H*3*,-/9 b8-3-M 36L0167 b .36b2J )6/8? 36b*,/8b6\ 0 [68*; b-[b-L9
Lb6 36[6 b 1b6L368\ -/b-+-|L6*;/9 -8 0336 0-,67?,-/80= H-/7* ,*/7-|K
,N .3*-+36[-b6,0M .-72)0; /7*L2J}** 236b,*,0*\9b79J}**/9 /7*L/8b0K
*; 236b,*,09 ‚ã^ƒ†
                              x
                                −
                                   y    2
                                      = 1,
                                            2
                                                                           ‚㕃
:L* b = c − a =               a    b    2   2
     2    2       2

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