Question 633534
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Hi,
y^(2)-9x^(2)-4y-54x-86=0   &#8658; (y-2)^2 - 9(x+3)^2 = 9
{{{(y-2)^2/3^2 - (x+3)^2/1^2 = 1}}}  C(-3,2)
{{{F[d] = sqrt(10)}}}  Foci (-3, 2 ±{{{sqrt(10)}}})
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