Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 90 стр.

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   °{ Èã ÓË® Ò² ¯È°°‚ÎËÓÒ«² ­‚Ëä ¹ºãÈȈ  ˆº B = 0  Ò ¯È°°äºˆ¯Òä ºˆËã Óº
        °ã‚ÈÒ∆≠Ò∆ ã«‚¯ÈmÓËÓÒ«mÒÈ Ax 2 + Cy 2 + 2 Dx + 2 Ey + F = 0 
         
         ‚°ˆ ∆≠wˆººÏÓÈÈˈˆº A ≠ 0 Ò C ≠ 0 Ò‚¯ÈmÓËÓÒËãÒÓÒÒäºÎˈ­©ˆ ¹Ë
                                                  D                                    E               D2 E 2
          ¯Ë¹Ò°ÈÓºmmÒË A x +         (        A   )   2
                                                              +C y+   (                C   )   2
                                                                                                   =
                                                                                                       A
                                                                                                         +
                                                                                                           C
                                                                                                              − F 

                         D2 E 2
          |­ºÏÓÈÒä P =   +    − F ˆºÈ¹Ë¯Ë®«}Óºmº®°Ò°ˆËäË}ºº¯ÒÓȈ
                         A   C
          
                                                         → →
                                                         e1′ = e1                                                   D
                                                         →     →                                           x = x′ − A
                                                        e ′2 = e 2     ;                                              
                                                                                                                      E
                                                   →        D  →   E →                                     y = y′ −
                                                  OO ′ = − e1 − e 2                                                 C
                                                             A     C
          
          ¹ºã‚Òä Ax ′ 2 + Cy ′ 2 = P Òºˆ}‚ÈÓ˹º°¯Ë°ˆmËÓÓº°ãË‚ˈˆº
          
                                                          x′2                              y′2
                                              ±                                ±                           = ±1 ;     P≠0
                                                           P                                P
                                                  (       | |
                                                           A          ) ( 2
                                                                                           | |
                                                                                            C      )   2

                                                                                                                              
                                                    x′    2
                                                                              y′   2
                                              ±                   ±                    =0 ;                P=0
                                                              2
                                                      |C |                    | A |2
          
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                         x′2      y′2                  x′2                y′2                          x′2      y′2
                             + 2 =0 ;      + 2 =1 ;      + 2 = −1 , Ë ∆ > 0
                         a2    b       a2    b       a2    b
                                                                                
                        x′ 2
                              y′ 2
                                      x′ 2
                                            y′ 2
                                                    x′ 2
                                                          y′2
                             − 2 =0 ;      − 2 =1 ;      − 2 = −1 , Ë ∆ < 0 .
                        a2    b       a2    b       a2    b
                                                      
          Ë¯m©Ë ¹«ˆ  ÒÏ ªˆÒ² °ã‚ÈËm °º˯ÎȈ°« m Áº¯ä‚ãÒ¯ºm}Ë ˆËº¯Ëä© È Ë°ˆº®
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          mÏÈÒäÓ©ä¹Ë¯Ëº­ºÏÓÈËÓÒËä¹Ë¯ËäËÓÓ©² x ′ Ò y ′ 
          
          
           °‚°ˆ ∆ wˆººÏÓÈÈˈˆº AC = 0 ˆºË°ˆ ãÒ­º A = 0 ãÒ­º C = 0  Óº
          ÓËmäË°ˆË ‚°ˆ  A = 0  Ë°ãÒªˆºÓˈÈ}ˆºmÏÈÒäÓº¹Ë¯Ëº­ºÏÓÈÒä¹Ë¯ËäËÓ
          Ó©Ë x ′ Ò y ′  ˆºÈ‚¯ÈmÓËÓÒËãÒÓÒÒ Cy 2 + 2 Dx + 2 Ey + F = 0 äºÎˈ­©ˆ ÏÈ
          ¹Ò°ÈÓºmmÒË
                                                                  E             E2
                                                  (
                                               C y+
                                                                  C   )   2
                                                                              =
                                                                                C
                                                                                   − F − 2 Dx                    , C ≠ 0 
                                                                                               

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