求弦中点轨迹方程.与圆有关的

2X^2-6X+2Y^2-8Y=39
设A(X1,Y2) B(X2,Y2) M(X,Y)
X=(X1+X2)/2 Y=(Y1+Y2)/2
PA=(X1 －3,Y1－4) PB=( X2－3,Y2－4)
PA•PB=0
X1X2 －3(X1+X2)+9+Y1Y2－4(Y1+Y2)+16=0
X1X2+Y1Y2－6X－8Y+25=0.①
X1^2+Y1^2=0.②
X2^2+Y2^2=0.③
②+③得
(X1+X2)^2－2X1X2+(Y1+Y2)^25－2Y1Y2=128
－X1X2－Y1Y2+2X^2+2Y^2=64.④
①+④得
2X^2-6X+2Y^2-8Y=39
即中点轨迹