SOLUTION: Find the standard form of the equation of the hyperbola with vertices at (2,0) and (6,0) and foci at (0,0) and (8,0).

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).