点P是椭圆x2/a2+y2/b2=1上一点,F1F2是焦点,且∠PF1F2=105,∠PF2F1=15,求e.
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![点P是椭圆x2/a2+y2/b2=1上一点,F1F2是焦点,且∠PF1F2=105,∠PF2F1=15,求e.](/uploads/image/z/5302569-57-9.jpg?t=%E7%82%B9P%E6%98%AF%E6%A4%AD%E5%9C%86x2%2Fa2%2By2%2Fb2%3D1%E4%B8%8A%E4%B8%80%E7%82%B9%2CF1F2%E6%98%AF%E7%84%A6%E7%82%B9%2C%E4%B8%94%E2%88%A0PF1F2%3D105%2C%E2%88%A0PF2F1%3D15%2C%E6%B1%82e.)
点P是椭圆x2/a2+y2/b2=1上一点,F1F2是焦点,且∠PF1F2=105,∠PF2F1=15,求e.
点P是椭圆x2/a2+y2/b2=1上一点,F1F2是焦点,且∠PF1F2=105,∠PF2F1=15,求e.
点P是椭圆x2/a2+y2/b2=1上一点,F1F2是焦点,且∠PF1F2=105,∠PF2F1=15,求e.
sin15°=sin(45°-30°)=(根号6-根号2)/4
cos15°=sin75°=sin105°=cos(45°-30°)=(根号6+根号2)/4
△PF1F2中
∠PF1F2=105°,∠PF2F1=15°
∠P=60°
利用正弦定理求出PF1=F1F2*sin15°/sin60°=(3根号2+根号6)c/3
PF2=F1F2*sin105°/sin60°=(3根号2-根号6)c/3
PF1+PF2=2根号2c=2a
e=c/a=根号2/2