已知椭圆1/2+y^2=1和椭圆外一点（0,2）,过这点引直线与椭圆交于A,B两点,求弦AB的中点P的轨迹方程

设A(X1,Y1),B(X2,Y2),AB中点P(X,Y) 则有:2X=X1+X2,2Y=Y1+Y2 X1^2/2+Y1^2=1 X2^2/2+Y2^2=1 二式相减得:(x1+x2)(x1-x2)/2+(y1+y2)(y1-y2)=0 即:2x(x1-x2)=-2y(y1-y2) (y1-y2)/(x1-x2)=-x/y 设A(0,2),则AP的斜率是:k=(y...