椭圆X2/25＋Y2/9＝1上一点M到左焦点距离是它到右焦点距离2倍，求M横坐标怎么做

Question

过程

Answer 1

右焦点(3,0),左焦点(-3,0)
设M点坐标(m,n)
(m-3)^2+n^2=4[(m+3)^2+n^2]
(m-3)^2-4(m+3)^2=3n^2
(m-3+2m+6)(m-3-2m-6)=3n^2
(m+1)(-m-9)=n^2
代入椭圆
m^2/25+(m+1)(-m-9)/16=1
9m^2+250m+625=0
m=-25,m=-25/9
m=-25,n无解
m=-25/9，n=±8√14/9
所以有两个点
(-25/9,8√14/9),(-25/9,-8√14/9)