椭圆x^2/a^2+y^2/b^2=1(焦点在x轴)与双曲线x^2/m^2-y^2/n^2=1有公共的焦点F1,F2

PF1+PF2=2a
PF1-PF2=2m
PF1=m+a PF2=a-m F1F2=2c a^2-b^2=m^2+n^2=c^2
cos F1PF2=[(a-m)^2+(a+m)^2-4c^2]/2(a^2-m^2)
=[(2a^2-2c^2) +(2m^2-2c^2)]/2(a^2-m^2)
=(b^2-n^2)/(b^2+n^2)
S△F1PF2=1/2 (m+a)(a-m)sin F1PF2=1/2 (b^2+n^2)√[1-(b^2-n^2)^2/(b^2+n^2)^2]=1/2√[(b^2+n^2)^2-(b^2-n^2)^2]=1/2 √(4b^2n^2)=bn