Question

写出适合条件的椭圆的标准方程：焦点在x轴上,焦距等于4,并且经过P(3,-2倍根号2)

Answer 1

F1(4,0) F2(-4,0) F1P=√((3-4)^2+(-2)^2*2)=3 F2P=√((3+4)^2+(-2)^2*2)=√57

2a=F1P+F2P a=(3+√57)/2 a*a=(33+ 6√57)/2 b*b=a*a-4*4=(1+ 6√57)/2

椭圆x^2/[(33+ 6√57)/2]+y^2/[(1+ 6√57)/2]=1