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(
问题描述:
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]
答
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即x*(2cosΘ)+y(2sinΘ)=4x0= r*cosΘ = 2cosΘ y0 = r*sinΘ = 2sinΘx*x0 + y*y0 = 4 = r^2故xcosΘ+ysinΘ=2是半圆x^2+y^...