过椭圆x^2/9+y^2/4=1内一点P(-1,1)作直线l交椭圆于A,B两点,点P为AB中点,则直线l方程为

Question

过椭圆x^2/9+y^2/4=1内一点P(-1,1)作直线l交椭圆于A,B两点,点P为AB中点,则直线l方程为

Answer 1

设点A（x1,y1）B（x2,y2）椭圆方程：4x²+9y²=364x1²+9y1²=364x2²+9y2²=36两式相减4(x1²-x2²)+9(y1²-y2²)=04(x1+x2)(x1-x2)+9(y1+y2)(y1-y2)=0这里x1+x2=-2y1+y2=...