Question

过点M(3,-1)且被电M平分的双曲线x²/4-y²=1的弦说在直线方程

Answer 1

弦ABxA+xB=2xM=2*3=6

yA+yB=2yM=2*(-1)=-2

k(AB)=(yA-yB)/(xA-xB)=(y+1)/(x-3)

[(xA)^2/4-(yA)^2]-[(xB)^2/4-(yB)^2]=1-1

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

6-4*(-2)*(yA-yB)/(xA-xB)=0

3+4*(y+1)/(x-3)=0

3x+4y+13=0