题目:(2013年第24届“希望杯”全国数学邀请赛试题高二第1试第20题)已知E,F是椭圆x29+y24=1的左右焦点,点P在椭圆周上,则→EP·→FP的取值范围是(以下称问题).大家都知道,椭圆或双曲线上一点与其两焦点组成的三角形叫做焦点三角形,它引人注目,是一个非常重要的几何量,潜在深厚积淀的文化底蕴,嵌入向量后,其性质更是多姿多彩,从而成为各种竞赛的热点,也是新课程新高考的重点.该问题是 Title: Known E, F is the left and right focus of the oval x29 + y24 = 1, the point P on the oval, then the “24th in the hope cup” national mathematics invitational competition high school first test 20 questions  → EP ·  → FP The range of values ​​(hereafter referred to as the problem) is as follows: Everyone knows that the triangle formed by a point on the ellipse or the hyperbola and its two focal points is called the focal triangle, which attracts attention and is a very important geometric quantity , The potential deep accumulation of cultural heritage, embedded in the vector, the nature is more colorful, and thus become a hot topic in all competitions, but also the focus of the new curriculum new entrance exam