设P点与椭圆交于两点A(x1,y1)B(x2,y2)
两点坐标带入椭圆方程
(x1)²/16+(y1)²/4=1
(x2)²/16+(y2)²/4=1
两式相减,(x1+x2)(x1-x2)+4(y1+y2)(y1-y2)=0
k=(y1-y2)/(x1-x2)=-(x1+x2)/4(y1+y2)=-2*2/(4*2*1)=-1/2
AB方程点斜式为y-1=-(x-2)/2
即 x+2y-4=0
答案：x+2y-4=0