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I need help changing the general form of an ellipses to standard form.

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2 Answers

(a ± b) = a2 ± 2ab + b2
4x2 + 24x + y2 - 10y - 3 = 0
4(x2 + 6x) + (y2 -10y) = 3                           
4(x2 + 2 · x · 3 + 9) + (y2 - 2 · 5 · y + 25) = 36 + 25 + 3
↑        times         ↑                                      ↑    
          = 36                                        ↑                ↑ 
                                                add 25 to the both sides  
4(x + 3)2 + (y + 5)2 = 64
    4(x + 3)2       (y + 5)2  
  —————  +  ————  = 1
        64               64    
                                        
    (x + 3)2       (y + 5)2
  —————  +  ————  =  1  
         8                64     

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