Question

已知F1,F2是双曲线X²/n-Y²=1的两个焦点,点P在双曲线上,且｜PF1｜+｜PF2｜=2根号

Answer 1

c^2=n+1

c=√(n+1)

F1F2^2=4(n+1)

｜PF1｜+｜PF2｜=2√[n+2]

|PF1|-|PF2|=2√n

PF1=√(n+2)+√n

PF1^2=2n+2+2√(n^2+2n)

PF2=√(n+2)+√n

PF2^2=2n+2-2√(n^2+2n)

PF1^2+PF2^2=4n+4=4(n+1)=F1F2^2

＜F1PF2=90