Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 315 стр.

UptoLike

Составители: 

Рубрика: 

¯ÒãºÎËÓÒË


vmº®°mÈ¹ºm˯²Óº°Ë®mº¯ºº¹º¯«
vmº®°mÈªããÒ¹Ò˰}ºº¹È¯ÈºãºÒÈ
°w ããÒ¹Ò˰}Ò® ¹È¯ÈºãºÒÓ˺¯ÈÓÒËÓÓÈ« ¹ºm˯²Óº° ¹º°}ºã} ÒÏ ˺ }È
ÓºÓÒ˰}ºº¯ÈmÓËÓÒ«°ãËËº
z
0
Ò ¹¯ÒÓÒäÈË°}ºãºÓººãÒËÏÓÈ
ËÓÒ«
°w ããÒ¹Ò˰}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ªããÒ¹Ò˰}ºº¹È¯ÈºãºÒÈ ¹ãº°}º° º¯ººÓÈãÓº® º°Ò
Oz
 ¹ºã
ÈË°«ëssqwx È ¹ãº°}º°«äÒ º¯ººÓÈãÓ©äÒ º°«ä
Ox
ÒãÒ
Oy
wjéjivsjsÈ
¹¯Òä˯¯È°°äÈ¯ÒmÈ« °Ë} ¹ãº°}º°
zz
=>
0
0
¹ºãÈËä°ãËËË¯ÈmÓËÓÒË
¹ãº°}º®ãÒÓÒÒ
=
=+
0
2
0
2
2
0
2
1
)2()2(
zz
zb
y
za
x

«mã«Ë®°« ªããÒ¹°ºä cÒ°
¯v¯º®°º¯ºÓ©°ËË
ÓÒË ¹ãº°}º°
0
yy =
¹¯ÒmºÒ }
¯ÈmÓËÓÒãÒÓÒÒ
=
=
0
2
2
0
22
)
(
2
2
yy
b
y
zax

«mã«Ë®°«¹È¯Èºãº®iã«°ãÈ«
°ËËÓÒ« ¹ãº°}º°
0
xx
=
¯Èm
ÓËÓÒË °ËËÓÒ« ÒäËË ÈÓÈãºÒÓ©®

x

z
èqxytvr¯
y

=
=
0
2
2
0
22
)
2
(2
xx
a
x
zby

¯ҹ˯ºãÒ˰}Ò®¹È¯ÈºãºÒ
|¹¯ËËãËÓÒË
¯
ºm˯²Óº° ÏÈÈmÈËäÈ«mÓË}ºº¯º®º¯ºÓº¯äÒ¯ºmÈÓÓº®°Ò°ËäË}º
º¯ÒÓÈ}ÈÓºÓÒ˰}Òä¯ÈmÓËÓÒËäÈ
;2
2
2
2
2
z
b
y
a
x
=
ab
>>
00,
ÓÈ
Ï©mÈË°«mqwnéivsq·nxrquwjéjivsvqlvu
¯ÒãºÎËÓÒË
vmº®°ˆmȹºm˯²Óº°ˆË®mˆº¯ºº¹º¯«}È



vmº®°ˆmȪããÒ¹ˆÒ˰}ºº¹È¯È­ºãºÒÈ
          
          
°wããÒ¹ˆÒ˰}Ò® ¹È¯È­ºãºÒ  Ó˺¯ÈÓÒËÓÓÈ« ¹ºm˯²Óº°ˆ  ¹º°}ºã }‚ ÒÏ Ëº }È
     ÓºÓÒ˰}ºº‚¯ÈmÓËÓÒ«°ãË‚ˈˆº z ≥ 0 Ò¹¯ÒÓÒäÈˈ°}ºã ‚ºÓº­ºã ÒËÏÓÈ
     ËÓÒ«

°wããÒ¹ˆÒ˰}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 

°{ °ËËÓÒÒ ªããÒ¹ˆÒ˰}ºº ¹È¯È­ºãºÒÈ ¹ãº°}º°ˆ  º¯ˆººÓÈã Óº® º°Ò Oz  ¹ºã‚
     Èˈ°« ëssqwx È ¹ãº°}º°ˆ«äÒ º¯ˆººÓÈã Ó©äÒ º°«ä Ox  ÒãÒ Oy   wjéjivsj sÈ
     ¹¯Òä˯¯È°°äȈ¯ÒmÈ«°Ë}‚‚ ¹ãº°}º°ˆ  z = z0 > 0 ¹ºã‚ÈËä°ãË‚ ËË‚¯ÈmÓËÓÒË
     ¹ãº°}º®ãÒÓÒÒ


                                                                     z                                          
                 x2             y2
                         +           =1                                                                                                        
             (a 2 z0 ) 2 (b 2 z0 ) 2                                                                                                         
                        z = z0                                                                                                                 
            
                                                                                                                                                
    
                                                                                                                                                
        «mã« Ë®°«      ªããÒ¹°ºä     cÒ°
                                                                                                                                                
        ¯ v¯‚º®°ˆº¯ºÓ©°ËË
                                                                                                                                                
        ÓÒË ¹ãº°}º°ˆ  y = y 0  ¹¯Òmº҈ }                                                                                                  
        ‚¯ÈmÓËÓÒ ãÒÓÒÒ                                                                                                                        
                 
                                                                                                                                                
                      2              y2                                                                                                        
                      x = 2a 2 ( z − 0 )                                                                                                       
                                    2b 2                                                                                                     
                           y = y0
                                                                                                                                               
                                                                                                                                               
        «mã« Ë®°«¹È¯È­ºãº®iã«°ã‚È«                                                                                                       
                                                                                                                                           
        °ËËÓÒ« ¹ãº°}º°ˆ  x = x 0  ‚¯Èm                          x                                                                         
        ÓËÓÒË °ËËÓÒ« ÒäËˈ ÈÓÈãºÒÓ©®                                                                                                     y
        mÒ                                                                           èqxytvr¯
                 2              x2
                 y = 2b 2 ( z − 0 )
                2a 2 
                      x = x0
                
             
             
             
¯€Ò¹Ë¯­ºãÒ˰}Ò®¹È¯È­ºãºÒ
             
             
    |¹¯ËËãËÓÒË          ºm˯²Óº°ˆ ÏÈÈmÈËäÈ«mÓË}ºˆº¯º®º¯ˆºÓº¯äÒ¯ºmÈÓÓº®°Ò°ˆËäË}º
    ¯
                                                                                                x2       y2
                          º¯ÒÓȈ }ÈÓºÓÒ˰}Òä ‚¯ÈmÓËÓÒËä mÒÈ                                   −        = 2 z;  a > 0, b > 0  ÓÈ
                                                                                                a2       b2
                          Ï©mÈˈ°«mqwnéivsq·nxrquwjéjivsvqlvu