过点A(4,0)引直线与椭圆x^2/16+y^2/9=1相交于M,N两点,求弦MN中点的轨迹?
问题描述:
过点A(4,0)引直线与椭圆x^2/16+y^2/9=1相交于M,N两点,求弦MN中点的轨迹?
答
设直线的斜率为k,过A的直线的方程为y = k(x-4)代入椭圆方程并整理:(9+16k²)x² -8*16k²x + 16²k² -9*16 = 0由韦达定理:x1+x2 = 8*16k²/(9+16k²)设MN的中点为B(x,y)2x = x1+x2 = ...