Hello, ^_^Engineer_Adam^_^!

Sorry, the book is correct . . .

Vertex at (6,5), conjugate axis along the x - axis

asymptotes: 5x - 6y - 30 and 5x + 6y - 30 = 0

My answer: .(y - 5)²/25 - (x - 6)²/36 .= .1

The book's answer: .(y²)/25 - (x - 6)²/36 .= .1

Who is correct?

You used (6,5) as the center . . . and it's avertex.

The two asymptotes intersect at the center.

. . 5x - 6y - 30 .= .0

. . 5x + 6y - 30 .= .0

Solve the system: the center is at (6,0).