以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的焦点为A,B以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的交点为A,B,与y轴的交点
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 10:36:35
![以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的焦点为A,B以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的交点为A,B,与y轴的交点](/uploads/image/z/1592336-56-6.jpg?t=%E4%BB%A5F1%2CF2%E4%B8%BA%E7%84%A6%E7%82%B9%E7%9A%84%E6%A4%AD%E5%9C%86X%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%EF%BC%9Eb%EF%BC%9E0%29%2C%E6%96%9C%E7%8E%87%E4%B8%BAk%E7%9A%84%E7%9B%B4%E7%BA%BFL%E8%BF%87%E5%B7%A6%E7%84%A6%E7%82%B9F1%E4%B8%94%E4%B8%8E%E6%A4%AD%E5%9C%86%E7%9A%84%E7%84%A6%E7%82%B9%E4%B8%BAA%2CB%E4%BB%A5F1%2CF2%E4%B8%BA%E7%84%A6%E7%82%B9%E7%9A%84%E6%A4%AD%E5%9C%86X%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%EF%BC%9Eb%EF%BC%9E0%29%2C%E6%96%9C%E7%8E%87%E4%B8%BAk%E7%9A%84%E7%9B%B4%E7%BA%BFL%E8%BF%87%E5%B7%A6%E7%84%A6%E7%82%B9F1%E4%B8%94%E4%B8%8E%E6%A4%AD%E5%9C%86%E7%9A%84%E4%BA%A4%E7%82%B9%E4%B8%BAA%2CB%2C%E4%B8%8Ey%E8%BD%B4%E7%9A%84%E4%BA%A4%E7%82%B9)
以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的焦点为A,B以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的交点为A,B,与y轴的交点
以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的焦点为A,B
以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的交点为A,B,与y轴的交点为M,又B为线段F1M的中点,若|K|≤√14/2,求椭圆离心率的取值范围.
以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的焦点为A,B以F1,F2为焦点的椭圆X^2/a^2+y^2/b^2=1(a>b>0),斜率为k的直线L过左焦点F1且与椭圆的交点为A,B,与y轴的交点
左焦点F1(-c,0),设过左焦点的直线为y=k(x+c)
x=0 => y=kc => M=M(0,kc)
B为F1M中点,则B=B(-c/2,kc/2)
B在椭圆上,则 (-c/2)^2/a^2+(kc/2)^2/b^2=1
1/4*c^2/a^2+k^2/4*c^2/b^2=1
1/4*c^2/a^2+k^2/4*c^2/(a^2-c^2)=1
e=c/a => e^2+k^2*e^2/(1-e^2)=4
=> k^2=(4-e^2)(1-e^2)/e^2
|k|≤√14/2 => k^2=(4-e^2)(1-e^2)/e^2≤14/4
=> 2(4-5e^2+e^4)≤7e^2
=> 2e^4-17e^2+8≤0
解得1/2≤e^2≤8
∵对于椭圆有0