Аналитическая геометрия. Часть I. Шурыгин В.В. - 94 стр.

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x
2
a
2
+
y
2
b
2
= 1
x = a cos t, y = b sin t.
x
y
a
b
x
M
y
M
M
t
a
b/a
b
a/b
S(t) OAM A(a; 0)
M(t)
t
S
0
(t) OMM
0
M
0
t + ∆t
∆t ∆t → 0 OMM
0
OMM
0
∆t S
0
(t)
OMM
0
∆t ∆t → 0
M
M
0
O
A
M(t)
O
.636;*830[-b68? ~770./
                                      x2 y 2
                                        +    =1                                        ‚`aƒ
/7*L2J}0; -+36[-;†                    a2 b2

                          x = a cos t,           y = b sin t.                          ‚``ƒ
Q*-;*830)*/10M /;/7 .636;*836 t b
236b,*,09N ‚``ƒ 9/*, 0[ 30/2,16 ò`\L*K               y

;-,/83032J}*:- 8-8 O618\ )8- ~770./
‚`aƒ ;-|*8 +8? .-72)*, 0[ -132|,-K                  b
                                                               M
/80 36L02/6 a /|680*; 1 -/0 6+/ 0// /              y     5           M

1-~OO0 0*,8-; b/a 070 36/89|*,0*;                            x   a x               M
-132|,-/80 36L02/6 b -8 -/0 -3L0,68
/ 1-~OO0 0*,8-; a/b =
   {)0/70; 8*.*3? L79 ~770./6 .7-K
}6L? S(t) /*18-36 OAM \ :L* A(a; 0) ·             Ç 0/= ò`=
8-)16 .*3*/*)*,09 ~770./6 / .-7-|0K
8*7?,-M )6/8?J -/0 6+/ 0// ‚b*3I0,6 ~770./6ƒ\ 6 M (t) · 8-)16 ~770.K
/6\ -.3*L*79*;69 /--8b*8/8b2J}0; [,6)*,0*; .636;*836 t = H3-0[b-L,69
O2,1 09 S (t) .3*L/86b79*8 .3*L*7 -8,-I*,09 .7-}6L0 /*18-36 OM M \
:L* M · 8-)16 ~770./6\ /--8b*8/8b2J}69 [,6)*,0J .636;*836 t + ∆t \ 1
          0                                                                              0


                 H                                         )
     0

∆t .30 ∆t → 0 = -/1-7?12 .7-}6L? /*18-36 OM M -870 6*8/9 -8 .7-K
}6L0 83*2:-7?,016 OM M ,6 +*/1-,*),- ;672J b*70)0,2 +-7** b/-1-:-
                                                                     0



.-39L16 )*; ∆t \ 8- .3-0[b-L,69 S (t) 36b,6 .3*L*72 -8,-I*,09 .7-}6L0
                              0

                                        0
83*2:-7?,016 OM M 1 ∆t .30 ∆t → 0 =
                     0



                         M0                                                M (t)
                                  M

               O                                                 O                 A



              Ç0/= _^=                                          Ç0/= _•=

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