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   

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

  = 8^2 + b^2

         89 = 64 + b^2

         25 = b^2

         b = ± 5  

 x^2/8^2 - y^2/5^2 = 1

 







 

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