17 solution: (I) connect MT, MA, MB, obviously m, t, a three-point * * line, and | MA |-| MT | = | AT | = 2cosθ. And | mt | = | MB|, so | ma |-| MB | = 2cosθ < 2sinθ = | ab |. Therefore, the trajectory of point M is a branch of hyperbola, the focus is on A and B, and the length of the real axis near point B is 2cosθ.

(ⅱ)f(θ)= | MN | min = | LK | = | LA |-| AK | = sinθ+cosθ-2 cosθ= sinθ-cosθ= .

From < θ < 0 < f (θ) < 1。

(iii) Let point M be the moving point on trajectory P, point N be the moving point on circle A, and let the maximum value of |MN| be g(θ) to find the value range of g(θ).

18. Syndrome: Left = (L2+A2) (L2-A2) (L2+B2) (L2+C2) = (A2+B2+C2+A2) (B2+C2+B2)