Question

已知定点A(0,1),B(0,-1),C(1,0),动点P满足：

Answer 1

(1)向量AP=(X,Y-1),向量BP=(X,Y+1),向量AP=(X+1,Y)

代入方程X^2+Y^2-1=K[(X+1)^2+Y^2]

(1-K)X^2-2KX+(1-K)Y^2-1-K=0

(2)当K=0时,X^2+Y^2-1=0

|2*向量AP+向量BP|=|(3X,3Y-1)|=根号[9X^2+(3Y-1)^2]

把X^2+Y^2-1=0代入

=根号(9-9Y^2+9Y^2-6Y+1)=根号(10-6Y)

当Y为-1时,最大为4

当Y为1时,最小为2