椭圆x²/9+y²/4=1求以(1,1)为中点的弦

1个回答

设端点为(x1,y1)和(x2,y2),斜率k=(y1-y2)/(x1-x2),由两点在椭圆上得
4(x1)²+9(y2)²=36,4(x2)²+9(y2)²=36,两式作差可得4(x1+x2)(x1-x2)+9(y1+y2)(y1-y2)=0
由于(1,1)是弦的中点,得x1+x2=2,y1+y2=2,于是解得k=-4/9
直线方程是(y-1)=k*(x-1),得4x+9y-13=0