过椭圆x^2+2y^2=4的左焦点作倾斜角为π/3的弦AB,则弦AB长为_数学解答

过椭圆x^2+2y^2=4的左焦点作倾斜角为π/3的弦AB,则弦AB长为

人气：108 ℃　时间：2019-10-23 04:51:24

解答

x^2+2y^2=4x^2/4+y^2/2=1a^2=4,b^2=2,c^2=a^2-b^2=2左焦点坐标:(-√2,0)倾斜角为π/3,Kab=tanπ/3=√3AB方程为：y= √3(x+√2)代入：x^2+2y^2=4得：x^2+2(√3(x+√2))^2=47x^2+12√2x+8=0x1+x2=-12√2/7,x1x2=8/7(x1...