Аналитическая геометрия. Шурыгин В.В. - 65 стр.

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x
2
a
2
+
y
2
b
2
= 1,
b
2
= a
2
− c
2
x
y
(a, 0)
(0, b)
F
2
(c, 0)F
1
(−c, 0)
M(x, y)
D
2
(x =
a
e
)(x = −
a
e
)D
1
d
2
d
1
r
2
r
1
M(x; y)
y
2
= b
2
−
b
2
a
2
x
2
y
2
M
|
−−→
MF
1
| =
p
(x + c)
2
+ y
2
|
−−→
MF
2
| =
p
(x − c)
2
+ y
2
|
−−→
MF
1
| = a +
c
a
x, |
−−→
MF
2
| = a −
c
a
x,
|
−−→
MF
1
| + |
−−→
MF
2
| = 2a M ∈ Φ
H*3*,-/9 -L0, 0[ 36L0167-b b .36b2J )6/8? 36b*,/8b6\ 0 [68*; b-[b-L9 Lb6
36[6 b 1b6L368\ -/b-+-L0;/9 -8 0336 0-,67?,-/80 = H-/7* ,*/7-|,N .3*K
-+36[-b6,0M .-72)0; /7*L2J}** 236b,*,0*\ 9b79J}**/9 /7*L/8b0*; 236bK
,*,09 ☘Ġ
                              x
                                 +
                                   2
                                   y
                                   2
                                     = 1,
                                               2

                                               2
                                                                    ‚ò_ƒ
:L* b = a − c =
    2     2      2
                              a    b

                                               y

                                               (0, b)
                     d1                                          M (x, y)
                                                                            d2
                              r1                               r2

                                                                                           x
                     F1 (−c, 0)                             F2 (c, 0)   (a, 0)



 (x = − ae )D1                                                                   D2 (x = ae )

                                    Ç0/= ڕ=
   €*832L,- 2+*L08?/9\ )ò_8- 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*;-;2 ~770./2 ‚ ƒ=
‡*M/8b08*7?,-\ 236b,*,0* ‚ò_ƒ ~1b0b67*,8,- /7*L2J}*;2† y = b − x =                             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;
                          2   2                                     2   2
           1                               2



                    −−→            c      −−→
                   |M F | = a + x, |M F | = a − x,
                          1
                                                       c
                                                        2
                                                                         ‚òãƒ
                                   a                   a
-812L6 /7*L2*8\ )8- |−M−F→| + |−M−F→| = 2a \ 8- */8? M ∈ Φ =
   „610; -+36[-;\ b/910M ~770./ ;-|*8 +8?          [6L6, b ,*1-8-3-M .39;-K
                          1            2


2:-7?,-M /0/8*;* 1--3L0,68 236b,*,0*; ‚ò_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* ‚ò_ƒ\
,6[b6*8/9 ‰ŠŒ¤Ž‰Š¦ L79 ~8-:- ~770./6=
                                      Á¾

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