Let F1 and F2 be the two focuses of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0). If F1, F2 and P (0, 2b) are the three vertices of an equilateral triangle, then the eccentricity of hyperbola is______ ．

Let F1 (- C, 0), F2 (C, 0), then | f1p | = C2 + 4B2, ∵ F1, F2, P (0, 2b) are the three vertices of an equilateral triangle, ∵ C2 + 4B2 = 2c, ∵ C2 + 4B2 = 4C2, ∵ C2 + 4 (c2-a2) = 4C2, ∵ C2 = 4a2, ∵ E2 = 4, ∵ e = 2

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1. It is known that the focus of the hyperbola X & # 178 / / A & # 178; - Y & # 178 / / B & # 178; = 1 is F1 and F2, And the point P on the hyperbola satisfies that Pf1 is perpendicular to PF2, Pf1 = 3, PF2 = 4?
2. The two focuses of hyperbola x squared / 9 - y squared / 16 = 1 are f1.f2, Point P is on hyperbola. If Pf1 is perpendicular to PF2, what is the distance from point P to X axis The answer in the book is 16 / 3
3. Let F 1 and F 2 be the two focuses of the hyperbola x ^ 2 / 4-y ^ 2 = 1, and point p be on the hyperbola If ∠ f1pf2 = 120 °, calculate the area of triangle f1pf2 Find the area of | Pf1 | PF2 | Find the minimum value of | Pf1 | PF2 |. It's wrong.
4. Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively. If P is on hyperbola and Pf1 vector * PF2 vector = 0, then | Pf1 vector + PF2 vector | =? The answer is 2 root 10. But I can't work it out
5. It is known that the points F1 and F2 are the left and right focal points of the hyperbola x square, a square, y square and b square = 1 respectively. The line passing through F2 and perpendicular to the X axis and If the hyperbola intersects at two points AB, if Abf1 is an acute triangle, then the value range of eccentricity of the triangle yes
6. As shown in the figure, it is known that F1 and F2 are the two focal points of the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 (a > 0, b > 0). Through F2, make a straight line perpendicular to the X axis, and the hyperbola intersects at point P, with the angle pf1f2 = 30 ° to solve the asymptote equation of the hyperbola
7. It is known that the points F1 and F2 are the left and right focus of hyperbola (x ^ 2) / (a ^ 2) - (y ^ 2) / (2) = 1 (a > 0), respectively. Through F2, the direction of the focus perpendicular to the X axis is made, and the intersection hyperbola is% 1 If △ f1ab is an equilateral triangle, the asymptote equation of the hyperbola is obtained
8. If the chord AB length of the left focus F1 passing through the hyperbola X / 16-y / 9 = 1 is 6, then the perimeter of △ abf2 (F2 is the right focus) is () A 28 B 22 C 14 D12
9. If the chord AB length of the left focus F1 passing through the hyperbola x216 − Y29 = 1 is 6, then the perimeter of △ abf2 (F2 is the right focus) is 6______ ．
10. Through hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1, the chord AB length of left focus F1 is 5?
11. If F1 and F2 are the two focal points of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1, if the distance between a point m on the hyperbola and one of its focal points is equal to 16, find the distance between the other focal point
12. If the distance from point P to focus F1 on hyperbola x236 − Y2100 = 1 is equal to 7, then the distance from point P to another focus F2 is 7______ ．
13. It is known that the left and right focal points of the hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1 are F1 and F2 respectively. If there is a point P on the hyperbola, then | Pf1 | times | PF2 | = 32 Try to find the area of triangle f1pf2
14. Given that F1 and F2 are the left and right focus of hyperbola C: x2-y2 = 1, point P is on C, and angle f1pf2 = 60 degrees, then the value of | Pf1 | multiplied by | PF2 | is How is it wrong to use the area bridge: 1 / 2 | Pf1 | multiply | PF2 | sin60 = b-cot60 / 2, which is different from the answer
15. It is known that F1 and F2 are the left and right focal points of hyperbola C: x2-y2 = 1, and point P is on C, ∠ f1pf2 = 60 °, then | Pf1 | · | PF2 | = () A. 2B. 4C. 6D. 8
16. There is a point P on the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1, F1F2 is the left and right focus of the hyperbola, the angle f1pf2 = 90 ° and the three sides of the triangle f1pf2 The eccentricity of hyperbola can be determined by the arithmetic sequence
17. Let F1F2 be the focus of the hyperbola X / 4 minus y, p be on the hyperbola, and
18. It is known that F1F2 is the two focal points of the hyperbola x2 / 4-y2 = 1, and the point P is on the hyperbola and satisfies the angle f1pf2 = 90 ° to find the s triangle f1pf2
19. F1F2 is the left and right focus of the hyperbola, P is a point on the hyperbola, angle f1pf2 = 60 degrees, triangle pf1f2 = 12 √ 3, and eccentricity is 2
20. It is known that the two focal points of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1 are F1 and F2 respectively, the point P is on the hyperbola, and | Pf1 | x | PF2 | = 32, so the size of angle f1pf2 is calculated