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Convert the equation 6x^2 - 3y^2 + 12x - 18y - 8 = 0 to the standard form of a hyperbola.

 Feb 11, 2021
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Multiply through by -1  and re-arrange to get

 

3y^2 + 18y       - 6x^2-12x   =   -8        complete the square for x and y

3 (y^2 + 6y)      - 6 (x^2 +2x)  = - 8

3 ( y+3)^2        - 6 (x+1)^2     = - 8 + 27 - 6   = 13

 

(y+3)^2  / 1/3    -  (x+1)^2 / 1/6      = 13     divide through by 13

 

(y+3)2 / (13/3)   -   (x+1)2 / (13/6 )   =   1       you can divde the denominators to get

 

(y+3)2 / (4.33)   - (x+1)2 / 2.1666    = 1                 if you need a square in the denominator

 

(y+3)/ (2.0817)2    -     (x+1)2 / (1.472)2   =1

 Feb 11, 2021

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