过P(-1,0)倾斜角为π/3的直线l与椭圆x²+2y²=4所截得的弦长为
问题描述：
过P(-1,0)倾斜角为π/3的直线l与椭圆x²+2y²=4所截得的弦长为
答
直线方程为y=tan(π/3)(x+1)=√3(x+1)代入椭圆得x^2+2*3(x+1)^2=47x^2+12x+2=0x1+x2=-12/7,x1x2=2/7弦长=√[(x1-x2)^2+(y1-y2)^2]=√(1+k^2)√(x1-x2)^2=√(1+k^2)√[(x1+x2)^2-4x1x2)]=2*√(144/49-8/7)=4√22/7...