椭圆焦点为F1(-c,0),F2(c,0),过E(a2/c,0)的直线与椭圆交与A ,B两点,F1A//F2B,且F1A=2F2B,(1)求AB的斜率(2)设点C与点A关于坐标原点对称,直线F2B上有的、一点H(m,n)(m不等于0)在三角形AF1C的外接圆
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![椭圆焦点为F1(-c,0),F2(c,0),过E(a2/c,0)的直线与椭圆交与A ,B两点,F1A//F2B,且F1A=2F2B,(1)求AB的斜率(2)设点C与点A关于坐标原点对称,直线F2B上有的、一点H(m,n)(m不等于0)在三角形AF1C的外接圆](/uploads/image/z/2490732-36-2.jpg?t=%E6%A4%AD%E5%9C%86%E7%84%A6%E7%82%B9%E4%B8%BAF1%28-c%2C0%29%2CF2%28c%2C0%29%2C%E8%BF%87E%28a2%2Fc%2C0%29%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%A4%AD%E5%9C%86%E4%BA%A4%E4%B8%8EA+%2CB%E4%B8%A4%E7%82%B9%2CF1A%2F%2FF2B%2C%E4%B8%94F1A%3D2F2B%2C%EF%BC%881%EF%BC%89%E6%B1%82AB%E7%9A%84%E6%96%9C%E7%8E%87%EF%BC%882%EF%BC%89%E8%AE%BE%E7%82%B9C%E4%B8%8E%E7%82%B9A%E5%85%B3%E4%BA%8E%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%E5%AF%B9%E7%A7%B0%2C%E7%9B%B4%E7%BA%BFF2B%E4%B8%8A%E6%9C%89%E7%9A%84%E3%80%81%E4%B8%80%E7%82%B9H%EF%BC%88m%2Cn%EF%BC%89%EF%BC%88m%E4%B8%8D%E7%AD%89%E4%BA%8E0%EF%BC%89%E5%9C%A8%E4%B8%89%E8%A7%92%E5%BD%A2AF1C%E7%9A%84%E5%A4%96%E6%8E%A5%E5%9C%86)
椭圆焦点为F1(-c,0),F2(c,0),过E(a2/c,0)的直线与椭圆交与A ,B两点,F1A//F2B,且F1A=2F2B,(1)求AB的斜率(2)设点C与点A关于坐标原点对称,直线F2B上有的、一点H(m,n)(m不等于0)在三角形AF1C的外接圆
椭圆焦点为F1(-c,0),F2(c,0),过E(a2/c,0)的直线与椭圆交与A ,B两点,F1A//F2B,且F1A=2F2B,(1)求AB的斜率
(2)设点C与点A关于坐标原点对称,直线F2B上有的、一点H(m,n)(m
不等于0)在三角形AF1C的外接圆上求n/m的值~
椭圆焦点为F1(-c,0),F2(c,0),过E(a2/c,0)的直线与椭圆交与A ,B两点,F1A//F2B,且F1A=2F2B,(1)求AB的斜率(2)设点C与点A关于坐标原点对称,直线F2B上有的、一点H(m,n)(m不等于0)在三角形AF1C的外接圆
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
设B为AE中点,x+3c=2x2⑤
③⑤☞x1=(9k²c²-2c²)/(2+3k²),x2=(9k²c²+2c²)/(2+3k²)☞k=±√2/3
当x1=0,x2=3c/2,当k=-√2/3,A(0,√2c),B(0,-√2c)
线段AF1的垂直分线l的方程:y-√2c/2=-√2/2*(x+c/2)
直线l与x轴的交点为(c/2,0),是△AF1C的外接圆的圆心
因此外接圆方程(x-c²/2)²+y²=(c+c/2)²
FB:y=√2(x-c) ☞n,m满足一下关系
(n-c²/2)²+m²=(c+c/2)²
m=√2(n-c),m≠0
所以k=-√2/3时,n/m=2√2/5