:(1)由已知,得 {ca=23a2c=92(2分)
解得 {a=3c=2.∴ {a2=9b2=5.(4分)
∴椭圆C的标准方程为 x29+y25=1;(6分)
(2)设点P(x1,y1)(-2<x1<3),
点M (92,y2),∵点F、P、M三点共线,x1≠-2,
∴ y1x1+2=y2132,y2=13y12(x1+2),∴点M (92,13y12(x1+2)).(8分)
∵ k1=y1x1-3,k2=13y13(x1+2),
∴k1•k2= y1x1-3×13y13(x1+2)= 13y123(x1+2)(x1-3).(10分)
∵点P在椭圆C上,∴ x129+y125=1,∴ y12=-59(x12-9).
∴k1•k2= 13×(-59)(x12-9)3(x1+2)(x1-3)= -6527×x1+3x1+2= -6527×(1+1x1+2).(12分)
∵-2<x1<3,∴ k1•k2<-269.∴k1•k2的取值范围是 (-∞,-269).(14分)