Hi im really struggling with a coordinate systems problem, i'd be very grateful if anyone could help me..

a hyperbola of the form (x squared over alpha squared) - (y squared over beta squared) = 1. has asymptotes with equation y^2=(m^2)(X^2) find an equation of the hyperbola in terms of x, y , a and m.
having done this part already i struggled with the next stage of the question:

a point P on the hyperbola is equidistant from one of its asymptotes and the x axis. prove that, for all values of m, P lies on the curve with equation
(x^2 - y^2)^2 = (4x^2)(x^2 - a^2)

ive a feeling this is to do with loci, but im completely flummoxed and dont know where to start!