題目中的圓的參數(shù)方程為：x = 3 + 2*cosθ ,y = 4 + 2*sinθ
即圓上點(diǎn)P的坐標(biāo)為(3 + 2*cosθ ,4 + 2*sinθ)
因此|AP|2+|BP|2 = (2 + 2*cosθ)² + (4 + 2*sinθ)² + (4 + 2*cosθ)² + (4 + 2*sinθ)² = 60 + (8/5)*((3/5)*cosθ + (4/5)*sinθ)
= 60 + (8/5)*sin(θ + a)
其中tan(a) = 3/4 ,因此若要取得最小值,需要使得sin(θ + a)最小,即sin(θ + a) = -1,即
(3/5)*cosθ + (4/5)*sinθ = -1 ,顯然當(dāng)cosθ = -(3/5) ,sinθ = -(4/5)的時(shí)候,達(dá)到最小值(或者將上式帶入圓的方程中解得cosθ和sinθ)因此可得：
x = 3 + 2*cosθ = 3 - 1.2 = 1.8
y = 4 + 2*sinθ = 4 - 1.6 = 2.4