Question

椭圆36分之x的平方＋9分之y的平方=1的弦被点2.2平分.这条弦所在的直线方程是

Answer 1

弦AB被点M(2,.2)平分

xA+xB=yA+yB=2*2=4

k(AB)=(yA-yB)/(xA-xB)=(y-2)/(x-2)

[(xA)^2/36+(yA)^2/9]-[(xB)^2/36+(yB)^2/9]=1-1

(xA+xB)*(xA-xB)+4*(yA+yB)*(yA-yB)=0

4+4*4*(yA-yB)/(xA-xB)=0

1+4*(y-2)/(x-2)=0

x+4y-10=0