Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 316 стр.

UptoLike

Составители: 

Рубрика: 


Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒ˰}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ

äÓºmkp
vmº®°mÈҹ˯ºãÒ˰}ºº¹È¯ÈºãºÒÈ
°ҹ˯ºãÒ˰}Ò® ¹È¯ÈºãºÒÓ˺¯ÈÓÒËÓÓÈ« ¹ºm˯²Óº° ¹º°}ºã} ÒÏ ˺
}ÈÓºÓÒ˰}ºº¯ÈmÓËÓÒ«°ãËËº
z
ãºË
°ҹ˯ºãÒ˰}Ò®¹È¯ÈºãºÒºãÈÈË
º°Ëmº®°ÒääË¯ÒË®ºÓº°ÒËãÓºº°Ò
Oz

¹ãº°}º°Óº®°ÒääË¯ÒË®ºÓº°ÒËãÓº}ºº¯ÒÓÈÓ©²¹ãº°}º°Ë®
Oxz
Ò
Oyz

°{°ËËÓÒÒҹ˯ºãÒ˰}ºº¹È¯ÈºãºÒ È¹ãº°}º°º¯ººÓÈãÓº®º°Ò}ºº¯ÒÓÈ
Oz
¹ºãÈË°«ҹ˯ºãÈÈ¹ãº°}º°«äÒº¯ººÓÈãÓ©äÒº°«ä
Ox
ÒãÒ
Oy
¹È
¯ÈºãÈcÒ°¯
sȹ¯Òä˯ ¯È°°äÈ¯ÒmÈ« °Ë}
¹ãº°}º°
] ]
!
¹ºãÈËä
°ãËËË ¯ÈmÓËÓÒË ãÒÓÒÒ
°ËËÓÒ«
=
=
0
2
0
2
2
0
2
1
)2()2(
zz
zb
y
za
x

«mã«Ë®°« ҹ˯ºãº® ¯Ò
0
0
<z
 ¯ÈmÓËÓÒËҹ˯ºã© 
ËÒäËmÒ
=
=
0
2
0
2
2
0
2
1
)2()2(
zz
zb
y
za
x

x
z
èqxytvr¯
y
v ¯º® °º¯ºÓ© ¹¯Ò °ËËÓÒÒ ҹ˯ºãÒ˰}ºº ¹È¯ÈºãºÒÈ ¹ãº°}º°
[ [
¹ºãÈËä¹ãº°}}¯Òm
=
=
0
2
2
0
22
)
2
(2
xx
a
x
zby
«mã«°«¹È¯Èºãº®iã«°ãÈ«
°ËËÓÒ«¹ãº°}º°
0
yy =
¯ÈmÓËÓÒËÈÓÈãºÒÓºÒÒäËËmÒ
=
+=
0
2
2
0
22
)
2
(2
yy
b
y
zax

jÏ ¹ºãËÓÓ©² ¯ÈmÓËÓÒ® °ãËË º ҹ˯ºãÒ˰}Ò® ¹È¯ÈºãºÒäºÎË©
¹ºãËÓ¹ º°¹ÈËãÓ©ä¹Ë¯ËäËËÓÒËäm¹¯º°¯ÈÓ°mË¹È¯Èºã©È}ºËËm˯
 Ë }  Ò Ò   } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈Ò˰}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



vmº®°ˆmÈҹ˯­ºãÒ˰}ºº¹È¯È­ºãºÒÈ
            
            
°€Ò¹Ë¯­ºãÒ˰}Ò® ¹È¯È­ºãºÒ    Ó˺¯ÈÓÒËÓÓÈ« ¹ºm˯²Óº°ˆ  ¹º°}ºã }‚ ÒÏ Ëº
      }ÈÓºÓÒ˰}ºº‚¯ÈmÓËÓÒ«°ãË‚ˈˆº z ã ­ºË


°€Ò¹Ë¯­ºãÒ˰}Ò®¹È¯È­ºãºÒº­ãÈÈˈ
      º°Ëmº®°Òääˈ¯ÒË®ºˆÓº°ÒˆËã Óºº°Ò Oz 
      ¹ãº°}º°ˆÓº®°Òääˈ¯ÒË®ºˆÓº°ÒˆËã Óº}ºº¯ÒÓȈө²¹ãº°}º°ˆË® Oxz Ò Oyz 
                  
                  
°{°ËËÓÒÒҹ˯­ºãÒ˰}ºº¹È¯È­ºãºÒȹ㺰}º°ˆ º¯ˆººÓÈã Óº®º°Ò}ºº¯ÒÓȈ
       Oz ¹ºã‚Èˈ°«ҹ˯­ºãÈȹ㺰}º°ˆ«äÒº¯ˆººÓÈã Ó©äÒº°«ä Ox ÒãÒ Oy  ¹È
      ¯È­ºãÈ cÒ°¯ 

                                                                 z                  
    sȹ¯Òä˯ ¯È°°äȈ¯ÒmÈ« °Ë}‚                                                   
    ‚ ¹ãº°}º°ˆ ] ]!¹ºã‚ÈËä                                                  
    °ãË‚ ËË ‚¯ÈmÓËÓÒË ãÒÓÒÒ                                                      
    °ËËÓÒ«                                                                          
              
                                                                                      
               x 2
                              y 2
                                                                                      
                       −             =1
          (a 2 z0 ) 2
                          (b 2 z0 ) 2                                               
                      z = z0
                                                                                      
                                                                                     
                                                                                     
    «mã« Ë®°« ҹ˯­ºãº® ¯Ò
                                                                                      
     z 0 < 0 ‚¯ÈmÓËÓÒËҹ˯­ºã©­‚                                                 
    ˈÒäˈ mÒ                                                                   
                                                                                     y
             x2              y2               x
                      −               = −1
       (a − 2 z ) 2 (b − 2 z ) 2           
                   0                     0
                         z = z0
                                                                                        èqxytvr¯
                                                                  
            
            
        v ¯‚º® °ˆº¯ºÓ© ¹¯Ò °ËËÓÒÒ ҹ˯­ºãÒ˰}ºº ¹È¯È­ºãºÒÈ ¹ãº°}º°ˆ                                                     [ [
                                  2                                         x02
                                  y = −2b 2 ( z −                               )
        ¹ºã‚ÈËä¹ãº°}‚ }¯Òm‚                   2a                           2 «mã«       ‚ °«¹È¯È­ºãº®iã«°ã‚È«
                                         =
                                       x    x  0
                                                                                     2              y2
                                                                                     x = 2a 2 ( z + 0 )
        °ËËÓÒ«¹ãº°}º°ˆ                y = y 0 ‚¯ÈmÓËÓÒËÈÓÈãºÒÓºÒÒäËˈmÒ                2b 2 
                                                                                          y = y0
                                                                                    
            
        jÏ ¹ºã‚ËÓÓ©² ‚¯ÈmÓËÓÒ® °ãË‚ˈ ˆº ҹ˯­ºãÒ˰}Ò® ¹È¯È­ºãºÒ äºÎˈ ­©ˆ 
        ¹ºã‚ËÓ¹º°ˆ‚¹ÈˆËã Ó©ä¹Ë¯Ëä˝ËÓÒËäm¹¯º°ˆ¯ÈÓ°ˆm˹ȯȭºã©ˆÈ}ˆºËËm˯