Given the foci of (8,0) and the difference of the focal radii = 6, find the equation of the hyperbola

Given :

The foci of hyperbola are (8,0) and (-8,0) .

The difference of the focal radii = 6.

To Find :

The equation of the hyperbola.

Solution :

We know, distance between foci is given by :

2c = 8 - (-8)

c = 8

Also, difference between the foci or focal distance is given by :

2a = 6

a = 3

Now, we know for hyperbola :

General equation of hyperbola is :

Hence, this is the required solution.