已知点P是椭圆x^2/100+y^2/36=1他到椭圆的左焦点F1的距离是它到右焦点F2的距离的3倍分别求点P与点F1,点P与点F2的距离 再求点P坐标

椭圆上的点到两个焦点距离和为2a
∵a^2=100
a=10
∴PF1+PF2=20
∵PF1=3PF2
∴PF1=15
PF2=5
F1(-8,0),F2(8,0)
设P(m,n)
PF1=3PF2
√[(m+8)^2+n^2]=3*√[(m-8)^2+n^2]
m^2+16m+64+n^2=9m^2-144m+576+9n^2
m^2-20m+64+n^2=0
∵m^2/100+n^2/36=1
n^2=36-36m^2/100
m^2-20m+64+36-36m^2/100=0
16m^2-500m+2500=0
m=25/4,m=25
∵a=10
m∴m=25/4
n^2=351/16
n=±3√39/4
∴P(25/4,3√39/4)或(25/4,-3√39/4)

椭圆上的点到两个焦点距离和==2aa^2=100a=10所以PF1+PF2=20PF1=3PF2所以PF1=15PF2=5F1(-8,0),F2(8,0)设P(m,n)PF1=3PF2根号[(m+8)^2+n^2]=3*根号[(m-8)^2+n^2]m^2+16m+64+n^2=9m^2-144m+576+9n^2m^2-20m+64+n^2=0因为...