来自关艳峰的问题
已知抛物线y2=2px(p>0),过点M(2p,0)的直线与抛物线相交于A,B,OA•OB=______.
已知抛物线y2=2px(p>0),过点M(2p,0)的直线与抛物线相交于A,B,
OA•
OB=______.
1回答
2020-05-08 13:48
已知抛物线y2=2px(p>0),过点M(2p,0)的直线与抛物线相交于A,B,OA•OB=______.
已知抛物线y2=2px(p>0),过点M(2p,0)的直线与抛物线相交于A,B,
OA•
OB=______.
设直线AB:x=ty+2p代入抛物线y2=2px消去x得,y2-2pty-4p2=0,设A(x1,y1),B(x2,y2)所以根据根与系数的关系可得:y1+y2=2pt,y1y2=-4p2∴OA•OB=x1x2+y1y2=(ty1+2p)(ty2+2p)+y1y2=t2y1y2+2pt(y1+y2)+4p2+...