Let p be a point on the ellipse X225 + y216 = 1, F 1 and F 2 be the focus. If ∠ f 1pf 2 = 60 °, then the area of △ f 1F 2 is______ ．

∵ the elliptic equation is X225 + y216 = 1, ∵ A2 = 25, B2 = 16. We can get a = 5, C2 = 25-16 = 9, that is, C = 3. ∵ P is a point on the ellipse X225 + y216 = 1, F1, F2 are the focus, ∵ according to the definition of ellipse, we can get Pf1 + PF2 = 2A = 10 ① In ∵ △ f1pf2, ∠ f1pf2 = 60 ° and F1F2 = 2C = 6 ∵. According to the cosine theorem, f1f22 = Pf12 + pf22-2pf1 · pf2cos60 ° = 36, that is, Pf12 + pf22-pf1 · PF2 = 36 ② Therefore, the answer is: 1633

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