A hyperbola is centered at C=(3,7). The vertices are (9,7) and (-3,7). The slopes of the asymptotes are m=+-5/6.
If you make a plot of the veritices and the center, you find----
The axis of the hyperbola is horizontal.
Since center is (3,7)
Since equation of asymptote is +-5/6 =. +-b/a
So, b= 5
So, the equation of hyperbola is
((x-3)^2)/36. - ((y-7)^2)/25. =1