Question

已知椭圆C的焦点F1(-2根号2,0)和F2(2根号2,0),长轴长6

Answer 1

设椭圆与直线的两交点为（x1,y1),(x2,y2),中点(x,y)

由题意的：

a=3,c=2根号2,b=1

x^2/9+y^2=1

1)x1^2/9+y1^2=1

2)x2^2/9+y2^2=1

1)-2)

1/9(x1-x2)(x1+x2)+(y1-y2)(y1+y2)=0

-1/9(x1+x2)/(y1+y2)=(y1-y2)/(x1-x2)

x=1/2(x1+x2),y=1/2(y1+y2)

-x/9y=(y-2)/x

x^2+9y^2-18y=0