9x² - 3y² - 36x - 6y + 12 = 0.


Complete the squares for x-terms and y-terms separately, step by step


(9x^2 - 36x) - (3y^2 + 6y) = -12


9*(x^2 - 4x) - 3*(y^2 + 2y) = -12


9*(x^2 -4x + 4) - 3*(y^2 + 2y + 1) = -12 + 9*4 - 3


9*(x-2)^2 - 3*(y+1)^2 = 21.


Divide both sides by 21


 -  = 1,   or equivalently


 -  = 1,


 -  = 1.    (Equation of a hyperbola)


Thus   a= ,  b= ,    and  c =  =  =  = .