椭圆x^2/5+y^2/4=1,a^2=5,b^2=4,c=1,左焦点F1(-1,0),
椭圆弦AB中点P(x,y)
xA+xB=2xP=2x,yA+yB=2y
k(AB)=(yA-yB)/(xA-xB)=y/(x+1)
x^2/5+y^2/4=1
4x^2+5y^2=20
4(xA)^2+5(yA)^2=20.(1)
4(xB)^2+5(yB)^2=20.(2)
(1)-(2):
4(xA+xB)*(xA-xB)+5(yA+yB)*(yA-yB)=0
4(xA+xB)+5(yA+yB)*(yA-yB)/(xA-xB)=0
4*2x+5*2y*y/(x+1)=0
弦中点的轨迹方程椭圆:(x+0.5)^2/0.25+y^2/0.2=1