Hi,

y^(2)-9x^(2)-4y-54x-86=0   ⇒ (y-2)^2 - 9(x+3)^2 = 9

  C(-3,2)

  Foci (-3, 2 ±)

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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