过椭圆x29+y24=1内一点M(2,0)引椭圆的动弦AB,则弦AB的中点N的轨迹方程是 _ .

问题描述:

过椭圆

x2
9
+
y2
4
=1内一点M(2,0)引椭圆的动弦AB,则弦AB的中点N的轨迹方程是 ___ .

设N(x,y),A(x1,y1),B(x2,y2),则x129+y124=1①,x229+y224=1②①-②,可得:(x1-x2)x9+(y1-y2)y4=0∴y1-y2x1-x2=-4x9y∵动弦AB过点M(2,0),弦AB的中点N,当M、N不重合时,有kAB=yx-2∴yx-2=-4x9y∴94y...