The length of the real axis of the hyperbola is 6 - 2 = 4,
and the real axis is the horizontal line y = 0 coinciding with x-axis.


The real semi-axis length is a =  = 2.


The center of the hyperbola is the midpoint between (0,0) and (8,0).
So, the center is the point (4,0).


The foci distance is 8 - 0 = 8.
The half of the foci distance is  = 4.
It is the distance from the hyperbola center to the focus point, which is traditionally called "c".


The imaginary semi-axis "b" is   =  =  = 12.
Hence, b = .


Thus the hyperbola standard form equation is

 -  = 1,


or, which is the same,  

 -  = 1.





Hyperbola  -  = 1  


The foci are (0,0) and (8,0).