Аналитическая геометрия. Шурыгин В.В. - 93 стр.

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i = 1, . . . , n Γ
r = r(t)
E
2
x = ρ cos ϕ
y = ρ sin ϕ
x = t
2
/2p y = t
O
i
j
t
A
x
y
M
x
2
+y
2
=
a
2
M
r = ae(t) t
i =
e
1
M e(t) = i cos t+j sin t
r = ae(t) ⇐⇒ x = a cos t, y = a sin t.
(α; β) t
M(t)
O t ∈ (−∞; +∞)
t
a
2
t OAM
A(a; 0)
cos
2
t + sin
2
t = 1
              \ 70,00 Γ = ˆ,0 861|* -.3*L*7*, ,*-L,-[,6),-\ [6b0/98 -8
i = 1, . . . , n
b+-36 236b,*,09 r = r(t) 0 -8 b+-36 3*.*36=
   “770./\   :0.*3+-72 0 .636+-72 ,6 .7-/1-/80 E 861|* ;-|,- [6L6b68?
36[70),;0 .636;*830)*/10;0 236b,*,09;0= €6.30;*3\ ;-|,- .-72)08?
                                                   2


.636;*830)*/10* 236b,*,09 ~80N 70,0M\ .*3*N-L9 b 0N .-793,N 236b,*,0K
9N ‚`_ƒ -8 .-793,N 1--3L0,68 1 .39;-2:-7?,; .- O-3;276; x = ρ cos ϕ \
              { )                                    )
y = ρ sin ϕ = 16 */8b* .636;*836\ [6L6J}*:- 8- 12 .636+-7\ - *b0L,-\
                                                                      )
;-|,- b[98? ** -3L0,682† x = t /2p \ y = t =
   { ~8-; .636:36O* 36//;6830b6J8/9 .636;*830)*/10* 236b,*,09 ~770.K
                                2



/6 0 :0.*3+-7\ b 1-8-3N .636;*83\ [6L6J}0M 8-)12\ .30,6L7*|6}2J
70,00\ 0;**8 */8*/8b*,,M :*-;*830)*/10M /;/7 =
   Ç6//;-830;    /,6)676 -132|,-/8? x +y =
      )
                                        2   2

a = „- 16 M ~8-M -132|,-/80 0;**8 36L02/K
 2
                                                           y
b*18-3 r = ae(t) \ :L* t · 2:-7\ ,6 1-8-3M                         M
,6L- .-b*3,28? ,6.36b79J}0M b*18-3 i =
                  )
e -/0 6+/ 0//\ 8-+ *:- ,6.36b7*,0* /-bK
                                                           j
                                                                  t
.67- / ,6.36b7*,0*; 36L02/6Kb*18-36 8-)10
 1
                                                          O            A x
M \6 e(t) = i cos t+j sin t · 132:-b69 b*18-3K
                                                                    i

,69 O2,1 09 ‚/;= 30/= òaƒ= „610; -+36[-;\
-132|,-/8? ;-|*8 +8? [6L6,6 .636;*830K
)*/10;0 236b,*,09;0                                      Ç0/= òa=
                r = ae(t)      ⇐⇒       x = a cos t, y = a sin t.        ‚`ãƒ
ˆ+76/8? )(α; β) 0[;*,*,09 .636;*836      t b+036*8/9 b [6b0/0;-/80 -8 2/7-K
b0M [6L6 0= €6.30;*3\ */70 8-)16 M (t) ,*.3*3b,- b36}6*8/9 b-132: 8-)K
10 O \ ;-|,- /)0868?\ )8- t ∈ (−∞; +∞) =
   H636;*83 t b 236b,*,09N ‚`ム0;**8 861|* /7*L2J}0M :*-;*830)*/10M
/;/7† )0/7- a t · ~8- 2Lb-*,,69 -30*,803-b6,,69 .7-}6L? /*18-36 OAM \
:L* A(a; 0) · 8-)16 .*3*/*)*,09 -132|,-/80 / .-7-|08*7?,-M )6/8?J -/0
                   2



6+/ 0//=
   { -/,-b* .636;*830)*/10N 236b,*,0M -132|,-/80 ‚`ム7*|08 830:-,-K
;*830)*/1-* 8-|L*/8b- cos t + sin t = 1 = “8- |* 8-|L*/8b- .-[b-79*8
                            2       2




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