Question 860398
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Hi,
Vertices (7,-1) and (1, -1) and foci (9,-1) and (-1, -1) Note: repeat of y = -1
Hyperbola {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}}opening right and left along y = -1
{{{(x-h)^2/a^2 - (y+1)^2/b^2 = 1}}} 
Vertices (7,-1) and (1, -1),  h = {{{(7+1)/2 }}}= 4  &#8658; foci are 3 units right and left of center (4, -1),  a = 3
{{{(x-4)^2/3^2 - (y+1)^2/b^2 = 1}}}
foci (9,-1)_ and (-1, -1). 5 units right and left of center (4, -1) {{{sqrt(9 + b^2)}}} = 5, b^2 = 16, b = 4
{{{(x-4)^2/3^2 - (y+1)^2/4^2 = 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
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