Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 300 стр.

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ºˆ¯ËÏ}ÈäÒ F1 A Ò F2 A 
            
                                           x
 ‘˺¯ËäÈ                ‚°ˆ  A              Ë°ˆ  ˆº}È ¹¯ÒÓÈãËÎȝȫ ªããÒ¹°‚ L ÏÈÈÓÓºä‚ }È
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                                                    →                            →
                                       ° r1 =| F1 A|= a − ε x ; r2 =| F2 A |= a + ε x ; 
                                       
                                                →         →
                                       ° | F1 A |+| F2 A | = 2a 
                                       
                                              ρ ( A, F1 ) ρ ( A, F2 )
                                       °              =            = ε 
                                              ρ ( A, D1 ) ρ ( A, D2 )
                                       
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                                                →                    →
                                       ° | F2 B |= p Ë F2 B º¯ˆººÓÈãËÓº°Ò Ox ° ∠α = ∠β 
            
            
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        °jäËËä r1 =             ( x − aε ) 2 + y 2        ; r2 = ( x + aε ) 2 + y 2 ‘ºÈ‚҈©mÈ«}ÈÓºÓÒ
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                                                                                             b2
                                           ri = ( x ± aε ) 2 + y 2 = ( x ± aε ) 2 +              2
                                                                                                     (a 2 − x 2 ) =
                                                                                             a
                                           = ( x ± aε ) 2 + (1 − ε 2 )(a 2 − x 2 ) =                                  

                                           = x 2 ± 2 xaε + a 2ε 2 + a 2 − a 2ε 2 − x 2 + x 2ε 2 =
                                           = a 2 ± 2 xaε + x 2ε 2 =| a ± ε x |.
                                                                             
            
                sº¹º°}ºã }‚ | x |≤ a Ò 0 ≤ ε < 1 ˆº D ± ε [ ≥ 0 Ò°ã˺mȈËã Óº
                        →                                  →
                r1 =| F1 A | = a − ε x ; r2 =| F2 A | = a + ε x 
           
           
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