若直线xcosΘ+ysinΘ=2(0≤Θ≤π)与椭圆x2+3y2=6有公共点,则Θ的取值范围(A[ 0,π ]B[ 0,π/4]C[3π/4,π]D[ 0,π/4]∪[3π/4,π]

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/28 12:23:42
若直线xcosΘ+ysinΘ=2(0≤Θ≤π)与椭圆x2+3y2=6有公共点,则Θ的取值范围(A[0,π]B[0,π/4]C[3π/4,π]D[0,π/4]∪[3π/4,π]若直线xcosΘ+ysin

若直线xcosΘ+ysinΘ=2(0≤Θ≤π)与椭圆x2+3y2=6有公共点,则Θ的取值范围(A[ 0,π ]B[ 0,π/4]C[3π/4,π]D[ 0,π/4]∪[3π/4,π]
若直线xcosΘ+ysinΘ=2(0≤Θ≤π)与椭圆x2+3y2=6有公共点,则Θ的取值范围(
A[ 0,π ]
B[ 0,π/4]
C[3π/4,π]
D[ 0,π/4]∪[3π/4,π]

若直线xcosΘ+ysinΘ=2(0≤Θ≤π)与椭圆x2+3y2=6有公共点,则Θ的取值范围(A[ 0,π ]B[ 0,π/4]C[3π/4,π]D[ 0,π/4]∪[3π/4,π]
重点在于 你要能看出来xcosΘ+ysinΘ=2是半圆x^2+y^2=4(y>=0)的切线
xcosΘ+ysinΘ=2

x*(2cosΘ)+y(2sinΘ)=4
x0= r*cosΘ = 2cosΘ y0 = r*sinΘ = 2sinΘ
x*x0 + y*y0 = 4 = r^2
故xcosΘ+ysinΘ=2是半圆x^2+y^2=4(y>=0)的切线
看到这里就请画个图吧
两曲线公切线有两条:
xcos(π/4)+ycos(π/4)=2
xcos(3π/4)+ycos(3π/4)=2
所以D