椭圆x^2/m^2+y^2=1(m>1)与双曲线x^2/n^2-y^2=1有公共的焦点F1,F2,P是它们的一个交点,求△F1PF2面积

椭圆与双曲线有公共焦点,即有m^2-1=n^2+1=c^2,即m^2-n^2=2,m^2+n^2=2(m^2-1)P为交点,则有椭圆方程：x^2/m^2+y^2=1 (1)双曲线方程：x^2/n^2-y^2=1 (2)(1)*m^2-(2)*n^2,可得(m^2+n^2)y^2=m^2-n^22(m^2-1)y^2=2|y(P)|=1...