题目

More than 700 business leaders, government officials and investors gathered in Mountain View, California in December,2012 to attend the Social Innovation（创新）Summit．It is an invitation-only conference aimed at finding new ways to deal with old problems． Traffic jam is a problem that Bruggemann hopes to solve．“Traffic is really bad in most countries and we thought there must be some way of doing something about it．”Last week, his team, winning the prize for its“nunav”traffic management system, received a Microsoft Imagine Cup Grant of ＄100，000．“Everyone t已知常数a＞0，向量=（0，a），=（1，0），经过原点O以+λ，为方向向量的直线与经过定点A（0，a）以i-2λc为方向向量的直线相交于点P，其中λ∈R．试问：是否存在两个定点E、F，使得|PE|+|PF|为定值．若存在，求出E、F的坐标；若不存在，说明理由．