Solution: Let the coordinates of P be (x0, y0) and the coordinates of point M be (x, y). Since m is the midpoint of AP and p is a point on the circle, the following coordinate relations are obtained: x=(4-x0)/2, y=y0/2, and x0=4-2x, y0=2y. X again? +y？ = 4, and the m-point trajectory equation is obtained by substitution.