Question

已知F1,F2是椭圆C:x²/a²+y²/b²=1(a>b>0)的两个焦点，P为椭圆C上

已知F1,F2是椭圆C:x²/a²+y²/b²=1(a>b>0)的两个焦点，P为椭圆C上一点，且向量PF1⊥向量PF2，若△PF1F2的面积为9，则b=

Answer 1

PF1^2+PF2^2=F1F2^2=4c^2
(1/2)PF1*PF2=9，PF1*PF2=18
PF1+PF2=2a，(PF1+PF2)^2=PF1^2+PF2^2+2PF1*PF2=4c^2+36=4a^2
b^2=a^2-c^2=9，b=3