设直线与椭圆的交点非别为(x1,y1),(x2,y2)
则y1^2/75+x1^2/25=1,y2^2/75+x2^2/25=1
两式相减,得
(y1^2-y2^2)/75+(x1^2-x2^2)/25=0
(y1-y2)(y1+y2)=-3(x1-x2)(x1+x2)
(y1-y2)/(x1-x2)=-3(x1+x2)/(y1+y2)
因为直线斜率为3,则(y1-y2)/(x1-x2)=3
两交点中点在直线x=1/2上,x1+x2=1
所以3=-3*1*(y1+y2)
(y1+y2)/2=-1/2
所以中点M坐标为(1/2,-1/2)