1、设直线与椭圆相交于A、B两点,A(x1,y1),B(x2,y2),x1^2/a^2+y1^2=1,(1),x2^2/a^2+y2^2=1,(2),(1)-(2)式,(x1^2-x2^2)/a^2+(y1^2-y2^2)=0,1/a^2+[(y1-y2)/(x1-x2)]*{[(y1+y2)/2]/[(x1+x2)/2]}=0,(3)其中(y1-y2)/(x1-x2)]=2,设平行弦动点坐标为(x,y),x=(x1+x2)/2,y=(y1+y2)/2,代入(3)式,1/a^2+2*y/x=0,∴中点轨迹方程为:y=-x/(2a^2).2、设弦中点坐标为(x,y),椭圆上任一点坐标为P(x0,y0),x= |