已知实数x,y满足x^2+y^2=3(y>=0),若m=(y+1)/(x+3),n=2x+y,则m,n的取值范围是?

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已知实数x,y满足x^2+y^2=3(y>=0),若m=(y+1)/(x+3),n=2x+y,则m,n的取值范围是?已知实数x,y满足x^2+y^2=3(y>=0),若m=(y+1)/(x+3),n=

已知实数x,y满足x^2+y^2=3(y>=0),若m=(y+1)/(x+3),n=2x+y,则m,n的取值范围是?
已知实数x,y满足x^2+y^2=3(y>=0),若m=(y+1)/(x+3),n=2x+y,则m,n的取值范围是?

已知实数x,y满足x^2+y^2=3(y>=0),若m=(y+1)/(x+3),n=2x+y,则m,n的取值范围是?
x^2+y^2=3(y>=0),
可得:x,y是构成在X轴上方的半圆.
-√3≤x≤√3,y≥0
所以m=(y+1)/(x+3)>0
即y=mx+3m-1
要使得直线y=mx+3m-1与半圆有交点,则
当直线过点(√3,0)时,m=(3-√3)/6
当直线与半圆相切时,把直线方程代入半圆中得到:
(m^2+1)x^2+2m(3m-1)x+(3m-1)^2-3=0
令△=0解得
m=(3+√21)/6或m=(3-√21)/6(舍去)
要使得直线y=mx+3m-1与半圆有交点,则
(3-√3)/6≤m≤(3+√21)/6
n=2x+y,y=-2x+n
当直线y=-2x+n经过点(-√3,0)时,n=-2√3
当直线y=-2x+n与半圆相切时,把直线方程代入半圆中
5x^2-4nx+n^2-3=0
令△=0解得
n=√15或n=-√15(舍去)
要使得直线y=-2x+n与半圆有交点,则
-2√3≤n≤√15

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