已知椭圆X²/a²+y²/b²=1(a>b>0)的两个焦点分别为F1(-c,0)和F2(c,0)(c>0),过点E(a²/c,0)的直线与椭圆相交于A,B两点,且F1A‖F2B,|F1A|=2|F2B|1.求椭圆离心率2.求直线AB的斜率
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![已知椭圆X²/a²+y²/b²=1(a>b>0)的两个焦点分别为F1(-c,0)和F2(c,0)(c>0),过点E(a²/c,0)的直线与椭圆相交于A,B两点,且F1A‖F2B,|F1A|=2|F2B|1.求椭圆离心率2.求直线AB的斜率](/uploads/image/z/5532027-51-7.jpg?t=%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86X%26sup2%3B%2Fa%26sup2%3B%2By%26sup2%3B%2Fb%26sup2%3B%3D1%EF%BC%88a%EF%BC%9Eb%EF%BC%9E0%EF%BC%89%E7%9A%84%E4%B8%A4%E4%B8%AA%E7%84%A6%E7%82%B9%E5%88%86%E5%88%AB%E4%B8%BAF1%EF%BC%88-c%2C0%EF%BC%89%E5%92%8CF2%EF%BC%88c%2C0%EF%BC%89%EF%BC%88c%EF%BC%9E0%29%2C%E8%BF%87%E7%82%B9E%EF%BC%88a%26sup2%3B%2Fc%2C0%EF%BC%89%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%A4%AD%E5%9C%86%E7%9B%B8%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E4%B8%94F1A%E2%80%96F2B%2C%7CF1A%7C%3D2%7CF2B%7C1.%E6%B1%82%E6%A4%AD%E5%9C%86%E7%A6%BB%E5%BF%83%E7%8E%872.%E6%B1%82%E7%9B%B4%E7%BA%BFAB%E7%9A%84%E6%96%9C%E7%8E%87)
已知椭圆X²/a²+y²/b²=1(a>b>0)的两个焦点分别为F1(-c,0)和F2(c,0)(c>0),过点E(a²/c,0)的直线与椭圆相交于A,B两点,且F1A‖F2B,|F1A|=2|F2B|1.求椭圆离心率2.求直线AB的斜率
已知椭圆X²/a²+y²/b²=1(a>b>0)的两个焦点分别为F1(-c,0)和F2(c,0)(c>0),过点E(a²/c,0)的直线与椭圆相交于A,B两点,且F1A‖F2B,|F1A|=2|F2B|
1.求椭圆离心率
2.求直线AB的斜率
已知椭圆X²/a²+y²/b²=1(a>b>0)的两个焦点分别为F1(-c,0)和F2(c,0)(c>0),过点E(a²/c,0)的直线与椭圆相交于A,B两点,且F1A‖F2B,|F1A|=2|F2B|1.求椭圆离心率2.求直线AB的斜率
由F1A//F2B且|F1A|=2|F2B|
☞|EF1|/|EF2|=|F2B|/|F1A|=1/2*(a²/c-c)/(a²/c+c)☞e=√3/3
2)b2=a2-c2=2c2
∴ 2x2+3y2=6c2
设直线AB:y=k(x-a²/c)=k(x-3c)①,设A(x1,y1)、B(x2,y2),
2x²+3y²=6c²②,①②☞(2+3k²)x²-18k²cx+27k²c²-6c²=2,Δ>0即-√3/3
(1) F1A‖F2B,|F1A|=2|F2B|
所以,a^2/c -c =2c
e=a/c=(根号3)/3
第二问就没想出来了