Solution: (1)∵ Two intersections A and B of straight line y=x-3 and coordinate axis,

Point b (0,3), point a (3,0),

Substitute the coordinates of a and b into parabola y=x2+bx-c to get:? c=？ 39+3b？ c=0，

Solution: c=3, b=-2,

Then the analytical formula of parabola is y = x2-2x-3;

(2) The analytical formula of parabola is y=x2-2x-3,

∴ c (- 1, 0), vertex d (1, 4),

Since point P is a moving point on a parabola, point P(a, a2-2a-3) is set.

∫S△APC:S△ACD = 5:4，

∴( 12×4×|a2-2a-3|):( 12×4×4)=5:4，

Sort it out: a2-2a-3=5 or a2-2a-3=-5 (from △ < 0, get the solution without real number and discard it).

Solution: a 1=4, a2=-2,

Then the coordinates of the point P that meets the conditions are p1(4,5), P2 (-2,5);

(3) As shown in the figure, a, b and d are the midpoint of M 1M3, M 1M2 and M2M3 respectively.

∵ Quadrilateral ADBM 1 is a parallelogram,

∴AB and M 1D are equally divided, that is, e is the midpoint of AB and e is the midpoint of m1d.

∫A(3，0)，B(0，-3)，

∴E(32,-32)，

∫D( 1，-4)，

∴M 1(2, 1)，

∴M2(-2,-7),M3(4,- 1)，

Then the coordinates of the point M satisfying the meaning of the question are: M 1 (2, 1), m2 (-2,7), M3 (4, 1).