Question 874059
{{{x^2 -y^2 =8x -12}}}
{{{x^2 -8x  -y^2 =-12}}}
{{{(x-4)^2 - y^2 = 4 }}}
{{{(x-4)^2/2^2 - y^2/4 = 1 }}}
centre (4,0) 
vertices (2,0) and (6,0)  
foci c = {{{sqrt(8)}}} (2+2√2, 0) and (2-2√2, 0)
equation of the asymptotes: m = ± 1,  y = 4x + 4, y = -4x - 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.  e = c/a.
Foci are  {{{sqrt(a^2+b^2)}}} =  c- units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a