Аналитическая геометрия. Шурыгин В.В. - 46 стр.

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A
B
C
−→
AC = Φ
−
π
3
(
−→
AB)
−→
AB = {4; 2}
−→
AC = {(4 cos(−
π
3
)−2 sin(−
π
3
)
2 cos(−
π
3
) + 4 sin(−
π
3
)} = {2 +
√
3; 1 −2
√
3}
r
C
= r
A
+
−→
AC
r
C
= {4 +
√
3; 2 − 2
√
3}
M
ω R
`
O A
C
x
y
t
M
{O; i, j}
M
` i
` j
`
C A
ω ` t = ∠ACM r
M
=
−→
OA +
−→
AC +
−−→
CM
|
−→
OA| = | ^ AM| = Rt
−→
OA = Rt i
−→
AC = R j
−−→
CM = R e(
3π
2
− t)
r
M
= Rt i + R j + R e(
3π
2
− t) = {Rt − R sin t; R − R cos t}
ω x
2
+y
2
= R
2
` x = R
M `
                               àxÿxXWxZ ­;= 30/2,-1 Æ^= H-/1-7?12 ,6
                     B
                            :*-;*830)*/1-M .7-/1-/80 .-7-|08*7?,;
                            /)086*8/9 b36}*,0* .3-80b )6/-b-M /83*7K
                            10\ 8- −AC         −→ —
                                       = Φ (AB) = ;**;† AB = {4; 2} =
     A                               →                      −→
                            ­7*L-b68*7?,-\ −AC − π3
                                               →
                                                 = {(4 cos(− )−2 sin(− ) Å
                                                                       π       π

                                                                       3} =
                                                           √         √ 3       3

       0/
      Ç = =Æ^        C
                            H
                            2 cos(−  ) π
                                       + 4 sin(− )} = π
                                                      {2 +   3; 1
                              -7?[29/? O-3;27-M r = r + AC \ ,6N-K
                                       3              3
                                                               − →
                                                                  − 2

                            L0; r = {4 + √3; 2 − 2√3} =   C        A

  ðÍwÍñÍ rZ ­-/86b08? 236b,*,09 836*18-300\ -.0/b6*;-M 8-)1-M M \
                                   C


7*|6}*M ,6 -132|,-/80 ω 36L02/6 R \1689}*M/9 +*[ /1-7?|*,09 .- L6,,-M
.39;-M ` ‚ 017-0L6ƒ=
  àxÿxXWxZ ­;= 30/2,-1 ƕ=
           y



               M       C
                   t

          O        A                                                   x
                            Ç0/= ƕ=
   {+*3*; -38-,-3;03-b6,,M 3*.*3 {O; i, j} ,6 .7-/1-/80 /7*L2J}0;
-+36[-;† [6 ,6)67- 3*.*36 b-[?;*; -L,- 0[ .-7-|*,0M 8-)10 M \ 1-:L6
-,6 -16[b6*8/9 ,6 .39;-M ` \ b 16)*/8b* b*18-36 i b-[?;*; *L0,0),M
,6.36b79J}0M b*18-3 .39;-M ` \ 0 +2L*; .3*L.-76:68?\ )8- b*18-3 j ,6K
.36b7*, -8 .39;-M ` b 82 /8-3-,2\ :L* 36/.-7-|*,6 -132|,-/8?= H2/8?
C · *,83 -132|,-/80 b O01/03-b6,,M ;-;*,8 b3*;*,0\ A · 8- 16
                                                                    )
16/6,09 ω 0 ` \ 6 t = ∠ACM = —;**;† r = −OA    → −→ −−→ ‚321-b-LK
                                                 + AC + CM
/8b2*;/9 .36b07-; [6;16,09 7-;6,-M®ƒ\ |OA| = | ^ AM | = Rt \ /7*K
                                          −
                                           M
                                             →
L-b68*7?,-\ −OA
              →          ‡ −→               −−→                H
                 = Rt i = 67**\ AC = R j \ CM = R e( − t) = -~8-;2
                                                              3π

r = Rt i + R j + R e( − t) = {Rt − R sin t; R − R cos t} =
                                                               2

   ðÍwÍñÍ ±Z H- -132|,-/80 ω \[6L6,,-M 236b,*,0*; x +y = R \ 16808/9
                       3π
 M                      2

+*[ /1-7?|*,09 .39;69 ` \ ,6)67?,-* .-7-|*,0* 1-8-3-M x = R = ­-/86b08?
                                                          2    2           2



236b,*,09 836*18-300\ -.0/b6*;-M 8-)1-M M \ 7*|6}*M ,6 ` \ .30,0;69
                                   ¸Á

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