Question 859896
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Hi,
{{{(x+1)^2/3^2 - (y+4)^2/7 = 1}}}  C(-1,-4) watch your x's and y's 
vertices 3 units right and left of Center: (-4,-4) and (2,-4)
foci sqrt(9+7) = 4.  Foci 4 units right and left of Center: (-5,-4)and (3, -4)
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