For the first part (and probably also for the second part), it will help you to show that if is the expression for the hyperbola, then the slopes of the asymptotes are , so that the equations of the asymptotes are .
Why? Solve the equation for the hyperbola with respect to y to get , and check that as x increases, the right hand side approaches .
The slope of your given asymptote is -2/5, so b/a = 2/5. Using the point P(6,2) as well gives you two equations with two unknowns.