Here's another way of arguing. The "asymptotes" of a hyperbola are the lines the hyperbola approaches for very very large values of x and y.
The equation of the hyperbola is as Earboth said. For very very large x and y those squares will each be far larger! Large enough that that "1" on the right side is negligible compared to them: For very very large x and y, that equation is very very close to from which we get and then . Taking x- 3= y- 8, y= x+ 5. Taking x- 3= -(y- 8), x- 3= -y+ 8, y= -x+ 11, the answer that Earboth gave.