Convert the equation 6x^2 - 3y^2 + 12x - 18y - 8 = 0 to the standard form of a hyperbola.
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 / (2.0817)2 - (x+1)2 / (1.472)2 =1
