Question 633559
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
y^(2)-9x^(2)-12y-36x-9=0   &#8658; (y-6)^2 - 9(x+2)^2 = 9
{{{(y-6)^2/3^2 - (x+2)^2/1^2 = 1}}} C(-2,6)
 V(-2, 9) and V(-2,3)
{{{F[d] = sqrt(10)}}}  Foci (-2, 6 ±{{{sqrt(10)}}}) 
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:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis
Foci {{{sqrt(a^2+b^2)}}}units units up and down from center, along x = h
& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a