SOLUTION: A hyperbola has vertices (8,0)and (-8,0)Its foci are located at (√(89),0) and(-√(89),0) identify the equation of this hyperbola. I honestly have no Idea how to solve

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