If there is an ellipse definition, the trajectory of m satisfies the definition of ellipse.

At this time, 2a = 2 √ 2, a = 2, c = 1, and b 2 = a-c 1 = 1.

The elliptic equation is x 2/2+y2 =1.

(2) Cos ∠ BAP = cos ∠ BAM = 2 ∠ 2/3，

So AM slope k=√2/4, and the equation is y=√2/4(x+ 1).

Substitute into elliptic equation to get

5x^2+2x-7=0

X= 1 or -7.

Because both p and m are in the first quadrant, x= 1.

The coordinate of m is (1, √2/2).