若椭圆mx^2+my^2与直线x+y-1=0相较于A B两点,过原点与线段AB中点的直线的斜率k为二分之根号二,则n/m=?详细过程答案是根号2/2
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![若椭圆mx^2+my^2与直线x+y-1=0相较于A B两点,过原点与线段AB中点的直线的斜率k为二分之根号二,则n/m=?详细过程答案是根号2/2](/uploads/image/z/4623311-47-1.jpg?t=%E8%8B%A5%E6%A4%AD%E5%9C%86mx%5E2%2Bmy%5E2%E4%B8%8E%E7%9B%B4%E7%BA%BFx%2By-1%3D0%E7%9B%B8%E8%BE%83%E4%BA%8EA+B%E4%B8%A4%E7%82%B9%2C%E8%BF%87%E5%8E%9F%E7%82%B9%E4%B8%8E%E7%BA%BF%E6%AE%B5AB%E4%B8%AD%E7%82%B9%E7%9A%84%E7%9B%B4%E7%BA%BF%E7%9A%84%E6%96%9C%E7%8E%87k%E4%B8%BA%E4%BA%8C%E5%88%86%E4%B9%8B%E6%A0%B9%E5%8F%B7%E4%BA%8C%2C%E5%88%99n%2Fm%3D%3F%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B%E7%AD%94%E6%A1%88%E6%98%AF%E6%A0%B9%E5%8F%B72%2F2)
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若椭圆mx^2+my^2与直线x+y-1=0相较于A B两点,过原点与线段AB中点的直线的斜率k为二分之根号二,则n/m=?详细过程答案是根号2/2
若椭圆mx^2+my^2与直线x+y-1=0相较于A B两点,过原点与线段AB中点的直线的斜率k为二分之根号二,则n/m=?
详细过程
答案是根号2/2
若椭圆mx^2+my^2与直线x+y-1=0相较于A B两点,过原点与线段AB中点的直线的斜率k为二分之根号二,则n/m=?详细过程答案是根号2/2
联立mx^2+ny^2=1
x+y-1=0
消去y,得
(m+n)x^2-2nx+n^2-1=0
A,B的横坐标x1,x2是上面方程的解
A,B中点的横坐标是(x1+x2)/2
x1+x2=2n/(m+n)
A,B中点的横坐标是n/(m+n)代入直线方程x+y-1=0
A,B中点的纵坐标是m/(m+n)
过原点与线段AB中点的直线的斜率k为
√2 /2
所以,n/m=√2
答案错了啊,你帮我检查一下有没有错,谢谢了!