(1) Assume M (x, y), A (a, 0), B (0, b),

From AM=λMB, we get (x-a, y) =λ(-x,b-y),

x?a＝?λxy＝λ(b?y), so a＝(1+λ)xb＝(1+λ)λy,

From a2+b2=25, we get x225(1+λ)2+y225λ2(1+λ)2=1.

①If λ=1, then the equation is x2+y2=254, and the trajectory is a circle;

②If 0＜λ＜1, then the trajectory E is expressed as the focus is on the x-axis

③If λ>1, then the trajectory E represents an ellipse with the focus on the y-axis.

(2) When λ=23, the trajectory equation is x29+y24=1,

Suppose C (x1, y1), D (x2, y2),

Suppose the slope of string CD is k, substitute in the difference, we get:

x12?x229-y12?y224=0,

From x1+x2=2, y1 +y2=2, we get k=-49,

The equation of ∴ straight line CD is y-1=-49 (x-1). After sorting it out, we get 4x+9y-13=0.