弦AB过抛物线y^2=2px的焦点,求弦AB中点M的轨迹方程
问题描述：
弦AB过抛物线y^2=2px的焦点,求弦AB中点M的轨迹方程
答
焦点(p/2,0)y=k(x-p/2)则k²(x²-px+p²/4)=2pxk²x²-(k²p+2p)x+p²/4=0x1+x2=(k²p+2p)/k²y1+y2=k(x1-p/2)+k(x2-p/2)=k(x1+x2)-kp=2p/kx=(x1+x2)/2,y=(y1+y2)/2y/x=2pk/(k&...