过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,求直线L的方过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,
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![过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,求直线L的方过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,](/uploads/image/z/9323185-49-5.jpg?t=%E8%BF%87%E6%A4%AD%E5%9C%86C%3A%28x%5E2%29%2F4%2By%5E2%3D1%E7%9A%84%E5%8F%B3%E7%84%A6%E7%82%B9%E4%BD%9C%E7%9B%B4%E7%BA%BFL%E4%BA%A4%E6%A4%AD%E5%9C%86C%E4%BA%8EM%2CN%E4%B8%A4%E7%82%B9%2C%E4%B8%94M%2CN%E5%88%B0%E7%9B%B4%E7%BA%BFx%3D4%2F%E2%88%9A3%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B9%8B%E5%92%8C%E4%B8%BA%E2%88%9A3%2C%E6%B1%82%E7%9B%B4%E7%BA%BFL%E7%9A%84%E6%96%B9%E8%BF%87%E6%A4%AD%E5%9C%86C%EF%BC%9A%28x%5E2%29%2F4%2By%5E2%3D1%E7%9A%84%E5%8F%B3%E7%84%A6%E7%82%B9%E4%BD%9C%E7%9B%B4%E7%BA%BFL%E4%BA%A4%E6%A4%AD%E5%9C%86C%E4%BA%8EM%2CN%E4%B8%A4%E7%82%B9%2C%E4%B8%94M%2CN%E5%88%B0%E7%9B%B4%E7%BA%BFx%3D4%2F%E2%88%9A3%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B9%8B%E5%92%8C%E4%B8%BA%E2%88%9A3%2C)
过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,求直线L的方过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,
过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,求直线L的方
过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,求直线L的方程.
过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,求直线L的方过椭圆C:(x^2)/4+y^2=1的右焦点作直线L交椭圆C于M,N两点,且M,N到直线x=4/√3的距离之和为√3,
设M(x1,y1),N(x2,y2),直线L的方程为x=√3或y=k(x-√3),M,N到直线x=4/√3的距离分别为d1,d2.
(1)若直线L的方程为x=√3,有x1=x2=√3,d1=d2=4/√3-√3=√3/3,
d1+d2=2√3/3≠√3,不合题设.
(2)若直线L的方程为y=k(x-√3),有
x^2+4k^2(x-√3)^2-4=0
整理得:(1+4k^2)x^2-8√3k^2x+12k^2-4=0
x1+x2=8√3k^2/(1+4k^2)
∵d1=4/√3-x1,d=4/√3-x2,d1+d2=√3
∴x1+x2=5/√3
∴8√3k^2/(1+4k^2)=5/√3
解得:k=±√5/2
∴直线L的方程为:y=±√5/2(x-√3),