Question

曲线x=cosθ y=-1+sinθ（θ为参数）与直线x=√3t y=a-3t（t为参数）有交点,求...

Answer 1

x=cosθ y=-1+sinθ

x=cosθ y+1=sinθ

消去参数得

x^2+(y+1)^2=1

x=√3t y=a-3t

x=√3t y-a=-3t

消去参数得

x/(y-a)=-√3/3

即

√3x+y-a=0

两者有交点,运用点到直线距离公式求圆心到直线的距离得

|-1-a|/2≤1

-3≤a≤1