Question

设椭圆X2/25+Y2/16=1上一点到左焦点的距离是4,F是该椭圆的左焦点,若点M满足向量OM=1/2(向量OP+向量

Answer 1

该椭圆a = 5,b = 4,c = 3,离心率e = c/a = 3/5,左准线x = -a^2/c = -25/3

设P点横坐标xP,根据椭圆第二定义,4/[xP-(-25/3)] = e,得xP = -5/3

代入椭圆方程得yP = +-2^(1/2)8/3

后面就自己做了吧~