已知实数x,y满足(x-2)^2+(y-1)^2=1,求z=((y+1)/x的最大值与最小值

题目

已知实数x,y满足(x-2)^2+(y-1)^2=1,求z=((y+1)/x的最大值与最小值

答案

令x=2+sina,y=1+cosa令(y+1)/x=(cosa+1)/(sina+2)=AAsina+2A=cosa+1Asina-cosa=1-2A√(A^2+1)sin(a+b)=1-2Asin(a+b)=(1-2A)/√(A^2+1)由-1≤sin(a+b)≤1,得-1≤(1-2A)/√(A^2+1)≤1(1-2A)^2/(A^2+1)≤1A(3A-4)≤00≤...