Question

已知实数x，y满足x^2+y^2-2y=0,求2x+y的取值范围。

Answer 1

x²+y²-2y=0 即 x²+(y-1)²=1 可设x=cosθ y=1+sinθ
则2x+y=2cosθ+sinθ+1=根号5倍的sin(θ+α)+1
∵sin(θ+α)的范围是[-1，1]，∴2x+y的取值范围是[1-根号5，1+根号5]

Answer 2

x^2+y^2-2y=0
x^2+(y-1)^2-1=0
x^2+(y-1)^2=1^2
以（0,1）为圆心，半径为1的圆，
-1<=x<=1,
-2<=2x<=2,
0<=y<=2,
-2<=2x+y<=4.