x²/25+y²/16=1的焦点,P为椭圆上一点.∠F1PF2=60°,求△PF1F2的面积
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x²/25+y²/16=1的焦点,P为椭圆上一点.∠F1PF2=60°,求△PF1F2的面积
x²/25+y²/16=1的焦点,P为椭圆上一点.∠F1PF2=60°,求△PF1F2的面积
x²/25+y²/16=1的焦点,P为椭圆上一点.∠F1PF2=60°,求△PF1F2的面积
x²/25+y²/16=1
a=5,b=4,∴ c=3
设PF1=m,PF2=n
(1)利用椭圆的定义 m+n=2a=10 ------------①
(2)利用余弦定理
F1F2²=m²+n²-2mncos60°
即 m²+n²-mn=36 ---------------------------------- ②
①²-②²
3mn=100-36=64
∴ mn=64/3
∴ △PF1F2的面积=(1/2)mn*sin60°=(1/2)*(64/3)*(√3/2)=16√3/3
16/3*根号(3)
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