Аналитическая геометрия. Шурыгин В.В. - 69 стр.

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M D P
M ρ
|
−−→
MF | = |
−−→
MA| α = β
MP A MP C |
−−→
MA| = |
−−→
MC|
M Φ
|
−−→
MF | = |
−−→
MC|.
E
2
D F
D F D
Φ M
F D
Φ = {M ∈ E
2
: |
−−→
MF | = dist(M, D)}.
M Φ r = |
−−→
MF |
M
d M ∈ Φ
M
M
e = 1
cos β = cos α
Φ
F Φ D p
dist(F, D) = p F
E
2
7936\ -.2}*,,-:- 0[ 8-)10 M ,6 .39;2J D \ 6 P · -/,-b6,0* .*3.*,L012K
7936\ -.2}*,,-:- 0[ 8-)10 M ,6 .7-/1-/8? ρ =
   H-/1-7?12 b/910* Lb* 16/68*7?,* 1 /O*3*\ .3-b*L*,,* 0[ -L,-M 0 8-M
|* 8-)10\ 36b,\ 8- |−M−→F | = |−M−→A| \ 6 .-/1-7?12 α = β \ 8- .39;-2:-7?,*
83*2:-7?,010 M P A 0 M P C 36b,\ -812L6 /7*L2*8\ )8- |−M−→A| = |−M−→C| = „6K
10; -+36[-;\ 16|L69 8-)16 M 1-,0)*/1-:- /*)*,09 Φ b 36//;6830b6*;-;
/72)6* 2L-b7*8b-39*8 /7*L2J}*;2 2/7-b0J†
                                 −−→        −−→
                                |M F | = |M C|.                           ‚_^ƒ
°,-|*/8b- 8-)*1 *b170L-b-M        .7-/1-/80\ 2L-b7*8b-39J}0N 2/7-b0J ‚_^ƒ\
,6[b6*8/9 ¡¬Š‹Š¦= „-),**\ /O-3;27032*; /7*L2J}** -.3*L*7*,0* =
   ϳTxwx™xXWxZ ›œžŸ  ¡‹Š‰ŠžŒ E ª‘ ¡£’£ D Œ žŠ¤‰ F ¥ Ž
¡Œª‹Ž»«£ ¡£’Š¦ D § ›¬Š‹Š¦  Ɋ‰œŠ’ F ªŒ ªŒŽ‰žŒŠ¦ D º
                                          2


¢‘”Žž£ ’Š»Žž”Š Φ ”ŽÐ žŠ¤Ž‰ M ¡‹Š‰ŠžŒ¥ ‹£ ‰ŠžŠ‘Ð žŠ£º
ŒŽ ªŠ žŠ¤‰Œ F ”Š žŠ£ŒÀ ªŠ ¡£’Š¦ D ¥ žŠ ŽžŸ¥
                                      −−→
                   Φ = {M ∈ E : |M F | = dist(M, D)}.
                                2
                                                                          ‚_•ƒ
   H2/8? 8-)16 M 7*|08 ,6 .636+-7* Φ = >0/7- r = |−M−→F | ,6[b6*8/9 Ɋº
‰‹Ÿ‘’ ªŒœŠ’ 8-)10 M =
   H2/8? d -[,6)6*8 36//8-9,0* -8 8-)10 M ∈ Φ L- L03*1830/= H-/1-7?12
L79 b/91-M .636+-7 -8,-I*,0* O-167?,-:- 36L02/6 ** 8-)10 M 1 36//8-K
9,0J -8 ~8-M 8-)10 L- L03*1830/ ,* [6b0/08 -8 b+-36 8-)10 M 0 36b,-
•\ 8- .- -.3*L*7*,0J /)086*;\ )8- b/9169 .636+-76 0;**8 ɝюžŒŒº
žŽž e = 1 = “8- -.3*L*7*,0* /-:76/2*8/9 0 / O-3;27-M ‚ò•ƒ\ .-/1-7?12 b
36//;6830b6*;-; /72)6* cos β = cos α =
   ,ÍXuXWñx¶yux STÍtXxXWx ³ÍTÍvu™UZ
   Ç6//;-830; .636+-72 Φ \ -.3*L*7*,,2J 161 ;,-|*/8b- 8-)*1 ‚_•ƒ= H2/8?
36//8-9,0* -8 O-12/6 F .636+-7 Φ L- ** L03*1830/ D 36b,- p \ 8- */8?
                H                          )
dist(F, D) = p = 39;69\ .3-N-L9}69 *3*[ O-12/ F 0 .*3.*,L012793,69
L03*1830/*\ 9b79*8/9 -/?J /0;;*8300 .636+-7= {+*3*; .39;-2:-7?,2J
/0/8*;2 1--3L0,68 ,6 .7-/1-/80 E \ b 1-8-3-M ~86 .39;69 9b79*8/9 -/?J
6+/ 0//\ ,6)67- 1--3L0,68 36b,-2L67*,- -8 O-12/6 0 L03*1830/\ 6 ,6K
                                    2


.36b7*,0* -/0 6+/ 0// /-b.6L6*8 / ,6.36b7*,0*; -8 L03*1830/ 1 O-12/2
                                         ÁÙ

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