Question 634918
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Hi,
{{{x^2/4-y^2/9=1}}}
{{{x^2/2^2-y^2/3^2=1}}}
Standard Form of an Equation of an Hyperbola opening right and  left is:
  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis
Foci are {{{sqrt(a^2+b^2)}}} units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 
center (0,0)
vertices (2,0) and (-2,0)
foci {{{f[d] = sqrt(13)}}}  ({{{sqrt(13)}}},0) and (-{{{sqrt(13)}}},0)
slopes of the asymptotes  m = ± 3/2