双曲线x^2-y^2=1①的两焦点为F1(-√2,0),F2(√2,0),点P在双曲线上,
PF1⊥PF2,
∴P在以F1F2为直径的圆:x^2+y^2=2②上.
②-①,2y^2=1,y^2=1/2,yP=土√2/2,
∴△F1PF2的面积=(1/2)|F1F2|*|yP|=(1/2)*2√2*√2/2=1.
双曲线x^2-y^2=1①的两焦点为F1(-√2,0),F2(√2,0),点P在双曲线上,
PF1⊥PF2,
∴P在以F1F2为直径的圆:x^2+y^2=2②上.
②-①,2y^2=1,y^2=1/2,yP=土√2/2,
∴△F1PF2的面积=(1/2)|F1F2|*|yP|=(1/2)*2√2*√2/2=1.