Hi,

y^(2)-9x^(2)-12y-36x-9=0   ⇒ (y-6)^2 - 9(x+2)^2 = 9

 C(-2,6)

 V(-2, 9) and V(-2,3)

  Foci (-2, 6 ±) 

Asymptotes: 

     y-6 = 3(x +2)   y = 3x+12

and  y-6 = -3(x+2)   y = -3x 

Standard Form of an Equation of an Hyperbola opening up and down is:

   with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis

Foci units units up and down from center, along x = h

& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a

 

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