设P是椭圆
|
P的参数坐标为(5cosθ,4sinθ);
坐标A(-5,0);F(3,0);
则
=(-5-5cosθ,0-4sinθ);PA
=(3-5cosθ,0-4sinθ);PF
则
•PA
+PF 1 4
•PA
=(-5-5cosθ)•(3-5cosθ)+16sin2θ+AF
(-5-5cosθ,-4sinθ)•(8,0)1 4
=(-5-5cosθ)(3-5cosθ)+16sin2θ+2(-5-5cosθ)
=9cos2θ-9≥-9.
故答案为:-9.
设P是椭圆
|
P的参数坐标为(5cosθ,4sinθ);
坐标A(-5,0);F(3,0);
则
=(-5-5cosθ,0-4sinθ);PA
=(3-5cosθ,0-4sinθ);PF
则
•PA
+PF 1 4
•PA
=(-5-5cosθ)•(3-5cosθ)+16sin2θ+AF
(-5-5cosθ,-4sinθ)•(8,0)1 4
=(-5-5cosθ)(3-5cosθ)+16sin2θ+2(-5-5cosθ)
=9cos2θ-9≥-9.
故答案为:-9.