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=
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![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=](/uploads/image/z/5300764-52-4.jpg?t=%E5%B7%B2%E7%9F%A5F1%2CF2%E6%98%AF%E6%A4%AD%E5%9C%86C%3Ax%26%23178%3B%2Fa%26%23178%3B%2By%26%23178%3B%2Fb%26%23178%3B%3D1%28a%3Eb%3E0%29%E7%9A%84%E4%B8%A4%E4%B8%AA%E7%84%A6%E7%82%B9%2CP%E4%B8%BA%E6%A4%AD%E5%9C%86C%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E4%B8%94%E5%90%91%E9%87%8FPF1%E2%8A%A5%E5%90%91%E9%87%8FPF2%2C%E8%8B%A5%E2%96%B3PF1F2%E7%9A%84%E9%9D%A2%E7%A7%AF%E4%B8%BA9%2C%E5%88%99b%3D)
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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=
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=
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=
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