Given the points a (1,2), B (3, - 5) and P as a moving point on the x-axis, find the coordinates of point P when the absolute value of the distance difference between P and a, B is the maximum

Given the points a (1,2), B (3, - 5) and P as a moving point on the x-axis, find the coordinates of point P when the absolute value of the distance difference between P and a, B is the maximum

Let B's symmetric point about X axis be B ′, connecting Pb ′, ab ′, then B ′ (3,5), Pb ′ = Pb, | pa-pb | = | pa-pb ′| ≤ ab ′, that is, when B ′, a and P are collinear, | pa-pb | is the largest. Let the analytic formula of the line ab ′ be y = KX + B, then 2 = K + B5 = 3K + B, and the solution of k = 32B = 12, | line ab ′