设弦交椭圆于点A（x1,y1）B（x2,y2）
椭圆方程：x²/25+y²/9=1,
x1²/25+y1²/9=1
x2²/25+y2²/9=1
两式相减
(x1²-x2²)/25+(y1²-y2²)/9=0
(x1+x2)(x1-x2)/25+(y1+y2)(y1-y2)/9=0
(y1-y2)/(x1-x2)=-9(x1+x2)/[25(y1+y2)]
设中点为P（x,y）
则x1+x2=2x,y1+y2=2y,
所以(y1-y2)/(x1-x2)=-9x/(25y).
又根据斜率公式可知：(y1-y2)/(x1-x2)=(y-2)/(x-1),
所以-9x/(25y) =(y-2)/(x-1),
即9x(x-1)+25y(y-2)=0,
9(x-1/2)²+25(y-1)²=109/4即为所求.