椭圆x05/36+y05/9=1的弦被点(4,2)所平分则弦所在的直线方程是

Question

椭圆x05/36+y05/9=1的弦被点(4,2)所平分则弦所在的直线方程是

Answer 1

椭圆：x²/36+y²/9=1
即9x²+36y²=36×9
设弦所在直线与椭圆交于A（x1,y1）B（x2,y2）
则
9x1²+36y1²=36×9
9x2²+36y2²=36×9
两式相减
9(x1²-x2²)+36(y1²-y2²)=0
9(x1+x2)(x1-x2)+36(y1+y2)(y1-y2)=0
弦中点（4,2）则x1+x2=8,y1+y2=4
(x1-x2)+2(y1-y2)=0
(y1-y2)/(x1-x2)=-1/2
即弦的斜率为-1/2
弦所在直线：y-2=-1/2(x-4)
x-4+2y-4=0
即x+2y-8=0