Question 391376
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Hi,         
vertices on the x-axis: (8,0)and (-8,0) Hyperbola opens right and left.

Standard Form of an Equation of an Hyperbola is  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} 
where Pt(h,k) is a center  with vertices 'a' units right and left of center
and asymptotes that pass thru the center with slope = ± b/a
In this example: center is (0,0) with a = 8
 x^2/8^2 - y^2/b^2 = 1
foci (c,0) and (-c,0) are (sqrt(89), 0),-sqrt(89), 0 }}}
 c, the distance from the center to the foci
  c^ = a^2 + b^2
 {{{sqrt(89)^2}}} = 8^2 + b^2
         89 = 64 + b^2
         25 = b^2
         b = ± 5  
 x^2/8^2 - y^2/5^2 = 1
 {{{x^2/64 - y^2/25 = 1}}}


<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/9/97/Hyperbola_properties.svg/200px-Hyperbola_properties.svg.png">