DP=m/3 or 3m

P(m+ 1, 3m) or (m+ 1, m/3).

When p is (m+ 1, 3m), AQ is; y=3x+3

And the other intersection of parabola (2,9) AP = m-1= ab = 2.

When m=3, it holds.

When p is (m+ 1, m/3), AQ is; y=x/3+ 1/3

And the other intersection of parabola (10/9,19/27) AP = m-1/9 = ab = 2.

When m= 19/9, it holds.