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)

a=9-3=6

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

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