Question

实数x,y满足x2+y2=4(y≥0),试求m=（根号3）x+y的取值范围

Answer 1

相当于求直线y=-√3x+m与圆x^2+y^2=4有公共点时m的取值范围

将y=-√3x+m代入x^2+y^2=4得：

x^2+(-√3x+m)^2=4

4x^2-2√3mx+m^2-4=0

判别式=(-2√3m)^2-4*4*(m^2-4)≥0

12m^2-16m^2+64≥0

4m^2≤64

m^2≤16

-4≤m≤4