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 = 8*16k²/(9+16k²)
2y = k(x1+x2-8) = -72k/(9+16k²)
(2x)/2y = x/y = -16k/9
9x + 16y = 0 (1)
B(x,y)在MN上,满足y = k(x-4),k = y/(x-4) (2)
(2)代入(1)：9x² -36x + 16y² = 0
整理得：(x-2)²/4 + y²/(9/4) = 1